Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.4 Expanding and Factoring Algebraic Expressions to score better marks in the exam.

## Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions

### Math in Focus Grade 6 Chapter 7 Lesson 7.4 Guided Practice Answer Key

**Expand each expression.**

Question 1.

3(x + 4)

Answer:

3x+12

Explanation:

3(x + 4)

= 3x + 3 x 4

= 3x + 12

Question 2.

6(2x + 3)

Answer:

12x + 18

Explanation:

6(2x + 3)

= 6 X 2x + 6 x 3

= 12x + 18

Question 3.

2(7 + 6x)

Answer: 14+ 12x

Explanation:

2(7 + 6x)

= 2 x 7 + 6x X 2

= 14 + 12x

Question 4.

5(y – 3)

Answer:

5y – 15

Explanation:

5(y – 3)

= 5y-15

Question 5.

4(4y – 1)

Answer:

16y – 4

Explanation:

4(4y – 1)

= 16y – 4

Question 6.

9(5x – 2)

Answer:

45x – 18

Explanation:

9(5x – 2)

= 9 x 5x – 2 x 9

= 45x – 18

**State whether each pair of expressions are equivalent.**

Question 7.

6(x + 5) and 6x + 30

Answer:

Yes, pair of expressions are equivalent

Explanation:

6(x + 5) and 6x + 30

6(x + 5) = 6x + 30

6(x + 5) and 6x + 30 are equal.

Question 8.

7(x + 3) and 21 + 7x

Answer:

Yes, pair of expressions are equivalent

Explanation:

7(x + 3) and 21 + 7x

7(x + 3) = 7x + 21

7x + 21 and 21 + 7x are equal.

Question 9.

4(y – 4) and 4y – 4

Answer:

NO, pair of expressions are not equivalent

Explanation:

4(y – 4) and 4y – 4

4(y – 4) = 4y – 16

4y – 16 is not equal to 4y – 4

Question 10.

3(y – 6) and 18 – 3y

Answer:

NO, pair of expressions are not equivalent

Explanation:

3(y – 6) and 18 – 3y

3(y – 6) = 3y – 18

3y – 18 is not equal to 18 – 3y

**Hands-On Activity**

Materials

- paper
- ruler
- scissors

RECOGNIZE THAT EXPANDED EXPRESSIONS ARE EQUIVALENT

STEP 1: Draw a rectangle that is 8 centimeters wide and more than 3 centimeters long on a piece of paper. Then cut out the rectangle.

Answer:

STEP 2: Find the area of the rectangle in terms of p.

Answer:

8p + 24 cm

Explanation:

Area of rectangle = Length x Breadth

= (p+3) x 8

= 8p + 24 cm

STEP 3: Then cut the rectangle into two rectangles A and B as shown.

STEP 4: Find the areas of rectangle A and rectangle B.

Answer:

24cm

Explanation:

Area of rectangle A = Length x Breadth

= p x 8

= 8p cm

Area of rectangle B = Length x Breadth

= 3 x 8

= 24 cm

STEP 5: Using your answers found in STEP 2 and STEP 4, state how the three areas are related.

Answer:

8p + 24 cm

Explanation:

Area of rectangle = Area of rectangle A + Area of rectangle B

8p + 24 cm = 8p + 24 cm

STEP 6: You may repeat the activity using rectangles of other sizes.

can be done with different size of rectangles

**Factor each expression.**

Question 11.

3x + 3

Answer:

3,(x + 1)

Explanation:

In the above expression 3 is common factor.

3 and (x + 1) are the factors of 3x + 3

Question 12.

4x + 6

Answer:

2 and (2x + 3)

Explanation:

In the above expression 2 is common factor.

2,(2x + 3) are the factors of 4x + 6

Question 13.

8 + 6y

Answer:

2 and (4 + 3y)

Explanation:

8+6y

In the above expression 2 is common factor.

2 and (4 + 3y) are the factors of 8 + 6y

Question 14.

5y – 10

Answer:

5, (y-2)

Explanation:

In the above expression 5 is common factor.

5y – 10 = 5(y – 2)

Question 15.

4 – 10z

Answer:

2(2 – 5z)

Explanation:

In the above expression 2 is common factor.

4 – 10z = 2(2 – 5z)

Question 16.

12 – 8x

Answer:

4, (3-2x)

Explanation:

In the above expression 4 is common factor.

12 – 8x = 4(3 – 2x)

Question 17.

8f + 6

Answer:

2 ,(4f+3)

Explanation:

In the above expression 2 is common factor.

8f + 6 = 2(4f + 3)

Question 18.

12t – 8

Answer:

4,(3f – 2)

Explanation:

In the above expression 4 is common factor.

12t – 8 = 4(3f – 2)

Question 19.

15 + 5q

Answer:

5, (3+q)

Explanation:

In the above expression 5 is common factor.

15 + 5q = 5(3 + q)

Question 20.

32m – 40

Answer:

8 and (4m-5)

Explanation:

In the above expression 8 is common.

8 and (4m – 5)are the factors of 32m – 40

**State whether each pair of expressions are equivalent.**

Question 21.

8x + 6 and 2(4x + 3)

Answer:

Yes, pair of expressions are equivalent.

Explanation:

8x + 6 and 2(4x + 3)

8x + 6 = 2(4x + 3)

2(4x + 3) and 2(4x + 3) are equal.

Question 22.

3(y + 6) and 18 + 3y

Answer:

Yes, pair of expressions are equivalent.

Explanation:

3(y + 6) and 18 + 3y

3(y + 6) = 3y + 18

3y + 18 = 18 + 3y are equal.

Question 23.

5x – 10 and 5(x – 5)

Answer:

No, pair of expressions are not equivalent.

Explanation:

5x – 10 and 5(x – 5)

5x – 10 = 5(x – 2)

5(x – 2) and 5(x – 5) are not equal.

Question 24.

4(y – 4) and 16 – 4y

Answer:

No, pair of expressions are not equivalent.

Explanation:

4(y – 4) and 16 – 4y

4(y – 4) = 4y – 16

4y – 16 is not equivalent to 16 – 4y

4(y – 4) and 16 – 4y are not equivalent.

Question 25.

3(x + 5) and 15 + 3x

Answer:

Yes, pair of expressions are not equivalent.

Explanation:

3(x + 5) and 15 + 3x

3(x + 5) = 3x + 15

3x + 15 is equal to 15 + 3x

3(x + 5) and 15 + 3x are equivalent expressions.

Question 26.

12 – 8y and 4(2y – 3)

Answer:

No, pair of expressions are not equivalent.

Explanation:

12 – 8y and 4(2y – 3)

12 – 8y = 4(3 – 2y)

12 – 8y and 4(2y – 3) are not equivalent.

### Math in Focus Course 1A Practice 7.4 Answer Key

**Expand each expression.**

Question 1.

5(x + 2)

Answer:

5x + 10

Explanation:

5(x + 2)

= 5 X x + 5 X 2

= 5x + 10

Question 2.

7(2x – 3)

Answer:

14x – 21

Explanation:

7(2x – 3)

= 7 X 2x – 7 X 3

= 14x – 21

Question 3.

4(y – 3)

Answer:

4y – 12

Explanation:

4(y – 3)

= 4 X y – 4 X 3

= 4y – 12

Question 4.

8(3y – 4)

Answer:

24y – 32

Explanation:

8(3y – 4)

= 8 X 3y – 8 X 4

= 24y – 32

Question 5.

3(x+ 11)

Answer:

3x + 33

Explanation:

3(x+ 11)

= 3 X x + 3 X 11

= 3x + 33

Question 6.

9(4x – 7)

Answer:

36x – 63

Explanation:

9(4x – 7)

= 9 X 4x – 9 X 7

= 36 x – 63

**Factor each expression.**

Question 7.

6p + 6

Answer:

6 , (p + 1)

Explanation:

6p + 6

Take 6 as common factor

6 (p + 1)

6, (p + 1) are the factors of 6p + 6

Question 8.

3p + 18

Answer:

3, (p + 6)

Explanation:

3p + 18

Take 3 as common factor

3 (p + 6)

3, (p+6) are the factors of 3p + 18

Question 9.

12 + 3q

Answer:

3, (4 + q)

Explanation:

12 + 3q

Take 3 as common factor

3 (4 + q)

3, (4 + q) are the factors of 12 + 3q

Question 10.

4w – 16

Answer:

4, (w – 4)

Explanation:

4w – 16

take 4 as common factor,

4 (w – 4)

4, (w – 4) are the factors of 4w – 16

Question 11.

14r – 8

Answer:

2, (7r – 4)

Explanation:

14r – 8

take 2 as common factor,

2 (7r – 4)

2, (7r – 4) are the factors of 14r – 8

Question 12.

12r – 12

Answer:

12, (r – 1)

Explanation:

12r – 12

take 12 as common factor,

12 (r – 1)

12, (r – 1) are the factors of 12r – 12

**State whether each pair of expressions are equivalent.**

Question 13.

4x + 12 and 4(x + 3)

Answer:

YES, pair of expressions are equivalent

Explanation:

4x + 12 and 4(x + 3)

4x + 12 and 4x + 12

both are equal

Question 14.

5(x – 1) and 5x – 1

Answer:

NO, pair of expressions are not equivalent

Explanation:

5(x – 1) and 5x – 1

5x – 5 and 5x – 1

both are not equal

Question 15.

7(5 + y) and 7y + 35

Answer:

YES, pair of expressions are equivalent

Explanation:

7(5 + y) and 7y + 35

35 + 7y and 7y + 35

both are equal

Question 16.

9(y – 2) and 18 – 9y

Answer:

NO, pair of expressions are not equivalent

Explanation:

9(y – 2) and 18 – 9y

9y – 18 and 18 – 9y

both are not equal

**Expand and simplify each expression.**

Question 17.

3(m + 2) + 4(6 + m)

Answer:

7m + 30

Explanation:

3(m + 2) + 4(6 + m)

= 3m + 6 + 24 +4m

= 7m + 30

Question 18.

5(2p + 5) + 4(2p – 3)

Answer:

18p+13

Explanation:

5(2p + 5) + 4(2p – 3)

= 10p + 25 + 8p – 12

= 18p + 13

Question 19.

4(6k + 7)+ 9 – 14k

Answer:

10k + 37

Explanation:

4(6k + 7)+ 9 – 14k

= 24k + 28 + 9 – 14k

= 10k + 37

**Simplify each expression. Then factor the expression.**

Question 20.

14x + 13 – 8x – 1

Answer:

6, (x+2)

Explanation:

14x + 13 – 8x – 1

= 14x – 8x + 13 – 1

= 6x + 12

= 6(x + 2)

6, (x + 2) are the factors of 14x + 13 – 8x – 1

Question 21.

8(y + 3) + 6 – 3y

Answer:

5, (y+6)

Explanation:

8(y + 3) + 6 – 3y

= 8y + 24 + 6 – 3y

= 8y – 3y + 24 + 6

= 5y + 30

= 5(y + 6)

5, (y + 6) are the factors of the 8(y + 3) + 6 – 3y

Question 22.

4(3z + 7) + 5(8 + 6z)

Answer:

2 , (21z+34)

Explanation:

4(3z + 7) + 5(8 + 6z)

= 12z + 28 + 40 + 30z

= 12z + 30z + 40 + 28

= 42z + 68

= 2 (21z + 34)

2 , (21z + 34) are the factors of 4(3z + 7) + 5(8 + 6z)

**Solve.**

Question 23.

Expand and simplify the expression 3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).

Answer:

28x

Explanation:

3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).

= 3x – 6 + 9x + 9 + 5 + 10x + 6x – 8.

= 3x + 9x + 10x + 6x – 6 +9 +5 – 8

= 28x + 0

= 28x

Question 24.

Are the two expressions equivalent? Justify your reasoning.

15(y + 6) + 10(y – 5) + 20(2y + 3)and 5(20 + 13y)

Answer:

Yes, the two expressions equivalent

Explanation:

15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)

= 15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)

= 15y + 90 + 10y – 50 +40y + 60 and 100 + 65y

= 65y + 100 and 100 + 65y

So, both are same.

Question 25.

A yard of lace costs w cents and a yard of fabric costs 40c more than the lace. Kimberly wants to buy one yard of lace and 2 yards of fabric. How much money will she need? Express your answer in terms of w.

Answer:

$80 w cents

Explanation:

cost of one yard of lace = w cents

cost of 2 yards of fabric = 2 × 40 = $80

Therefore, the total money needed is $80 + w cents

= $80 w cents

Question 26.

The average weight of 6 packages ¡s (9m + 8) pounds. 2 more packages, with weights of (12m + 1 2) pounds and (14m + 12) pounds, are added to the original 6 packages. Find the average weight of the 8 packages.

Answer:

10m + 9

Explanation:

9m + 8 is the average weight of the 6 packages = 54m + 48

12m + 12 and 14m + 12 is added

12m+12+14m+12 = 26m + 24

26m + 24 is added to the 54m + 48

= 54m + 26m + 48 + 24

= 80m + 72

the average weight of the 8 packages is = (80m + 72)/8 = 10m + 9

Question 27.

The figure shows two rectangles joined to form rectangle ABCD.

a) Write the length of \(\overline{B C}\) in terms of x. Then write an expression for the area of the rectangle ABCD in terms of x.

Answer:

Area =3x + 6 cm

Explanation:

the length of \(\overline{B C}\) in terms of x = x + 2

an expression for the area of the rectangle ABCD in terms of x

= x + 2 X 3

= (x + 2)3

= 3x + 6cm

b) Write an expression for the area of each of the two smaller rectangles.

Answer:

6 cm

Explanation:

the area of each of the two smaller rectangles

= 2 x 3 = 6cm

c) **Math Journal** Explain how you can use your answers in a) and b) to show that the following expressions are equivalent. 3x + 6 and 3(x + 2)

Answer:

Yes, both are equivalent

Explanation:

3x + 6 and 3(x + 2)

3(x + 2) can be written as 3x + 6

So, both are equal.