Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 3 Lesson 3.5 Factoring Algebraic Expressions to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 3 Lesson 3.5 Answer Key Factoring Algebraic Expressions

### Math in Focus Grade 7 Chapter 3 Lesson 3.5 Guided Practice Answer Key

**Copy and complete to factor the expression.
**Question 1.

2j – 10 k

2j – 10k = + () Rewrite the expression.

= () + () The GCF of 2j and -10k is 2.

= Factor 2 from each term.

Answer:

2j – 10 k = 2 (-5k + j) or 2 (j – 5k).

Explanation:

2j – 10 k = -10k + 2j

= 2 (-5k) + 2 (j)

= 2 (-5k + j) or 2 (j – 5k)

**Factor each expression.
**Question 2.

6a – 18b

Answer:

6a – 18b = 3 (2a – 6b).

Explanation:

6a – 18b = 3 (2a) + 3 (-6b)

= 3 (2a – 6b).

Question 3.

8p – 12q

Answer:

8p – 12q = 4 (2p – 3q).

Explanation:

8p – 12q = 4 (2p) + 4 (-3q)

= 4 (2p – 3q).

Question 4.

-5x – 3

Answer:

-5x – 3 = -1 (5x + 3).

Explanation:

-5x – 3 = -1 (5x) -1 (3)

= -1 (5x + 3).

Question 5.

-3f – 6

Answer:

-3f – 6 = -3 (f + 2).

Explanation:

-3f – 6 = -3 (f) – 3 (2)

= -3 (f + 2).

Question 6.

-8p – 10q

Answer:

-8p – 10q = -2 (4p + 5q).

Explanation:

-8p – 10q = -2 (4p) – 2 (5q)

= -2 (4p + 5q)

### Math in Focus Course 2A Practice 3.5 Answer Key

**Factor each expression with two terms.
**Question 1.

2x + 8

Answer:

2x + 8 = 2 (x + 4).

Explanation:

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

= 2 (x + 4).

Question 2.

5a + 5

Answer:

5a + 5 = 5 (a + 1).

Explanation:

5a + 5 = 5 (a) + 5 (1)

= 5 (a + 1).

Question 3.

3x – 12

Answer:

3x – 12 = 3 (x – 4).

Explanation:

3x – 12 = 3 (x) + 3 (-4)

= 3 (x – 4).

Question 4.

4x – 16

Answer:

4x – 16 = 4 (x – 4).

Explanation:

4x – 16 = 4 (x) + 4 (-4)

= 4 (x – 4).

Question 5.

2x + 8y

Answer:

2x + 8y = 2 (x + 4y).

Explanation:

2x + 8y = 2 (x) + 2 (4y)

= 2 (x + 4y).

Question 6.

7a + 7b

Answer:

7a + 7b = 7 (a + b).

Explanation:

7a + 7b = 7 (a) + 7 (b)

= 7 (a + b).

Question 7.

5p + 15q

Answer:

5p + 15q = 5 (p + 3q).

Explanation:

5p + 15q = 5 (p) + 5 (3q)

= 5 (p + 3q).

Question 8.

14w + 49m

Answer:

14w + 49m = 7 (2w + 7m).

Explanation:

14w + 49m = 7 (2w) + 7 (7m)

= 7 (2w + 7m).

Question 9.

4j – 16 k

Answer:

4j – 16 k = 4 (j – 4k).

Explanation:

4j – 16 k = 4(j) + 4(-4k)

= 4 (j – 4k).

Question 10.

8t – 32u

Answer:

8t – 32u = 8 (t – 4u).

Explanation:

8t – 32u = 8(t) + 8 (-4u)

= 8 (t – 4u).

Question 11.

2a – 10p

Answer:

2a – 10p = 2 (a – 5p).

Explanation:

2a – 10p = 2 (a) + 2 (-5p)

= 2(a – 5p).

Question 12.

9h – 45f

Answer:

9h – 45f = 9 (h – 5f).

Explanation:

9h – 45f = 9 (h) + 9 (-5f)

= 9(h – 5f).

**Factor each expression with negative terms.
**Question 13.

-p – 2

Answer:

-p – 2 = -1 (p + 2).

Explanation:

-p – 2 = -1 (p) – 1(2)

= -1 (p + 2).

Question 14.

-x – 5

Answer:

-x – 5 = -1 (x + 5).

Explanation:

-x – 5 = -1 (x) -1 (5)

= -1 (x + 5).

Question 15.

-2d – 7

Answer:

-2d – 7 = -1 (2d + 7).

Explanation:

-2d – 7 = -1 (2d) – 1(7)

= -1 (2d + 7).

Question 16.

– 4y – 11

Answer:

– 4y – 11 = -1 (4y + 11).

Explanation:

– 4y – 11 = -1 (4y) – 1(11)

= -1 (4y + 11).

Question 17.

-3a – 6

Answer:

-3a – 6 = -3 ( a + 2).

Explanation:

-3a – 6 = -3 (a) – 3 (2)

= -3 ( a + 2).

Question 18.

-4x – 20

Answer:

-4x – 20 = -4 (x + 5).

Explanation:

-4x – 20 = -4(x) – 4 (5)

= -4 (x + 5).

Question 19.

-5k – 25

Answer:

-5k – 25 = -5 (k + 5).

Explanation:

-5k – 25 = -5 (k) – 5( 5)

= -5 (k + 5).

Question 20.

-7u – 49

Answer:

-7u – 49 = -7 (u + 7).

Explanation:

-7u – 49 = -7 (u) – 7 (7)

= -7 (u + 7).

Question 21.

-1 – 4n

Answer:

-1 – 4n = -1 (1 + 4n).

Explanation:

-1 – 4n = -1 (1) – 1(4n)

= -1 (1 + 4n).

Question 22.

-3 – 6a

Answer:

-3 – 6a = -3 (1 + 2a).

Explanation:

-3 – 6a = -3 (1) – 3( 2a)

= -3 (1 + 2a).

Question 23.

-12x – 16y

Answer:

-12x – 16y = -4 (3x + 4y).

Explanation:

-12x – 16y = -4 (3x) – 4(4y)

= -4 (3x + 4y).

Question 24.

-25m – 10n

Answer:

-25m – 10n = -5 (5m + 2n).

Explanation:

-25m – 10n = -5 (5m) – 5(2n)

= -5 (5m + 2n).

**Factor each expression with three terms.
**Question 25.

4x + 4y + 8

Answer:

4x + 4y + 8 = 4 (x + y + 2).

Explanation:

4x + 4y + 8 = 4(x) + 4(y) + 4(2)

= 4 (x + y + 2).

Question 26.

2a + 6b + 4

Answer:

2a + 6b + 4 = 2( a + 3b + 2).

Explanation:

2a + 6b + 4 = 2(a) + 2(3b) + 2(2)

= 2( a + 3b + 2).

Question 27.

5p + 10q + 10

Answer:

5p + 10q + 10 = 5(p + 2q + 2).

Explanation:

5p + 10q + 10 = 5(p) + 5(2q) + 5(2)

= 5(p + 2q + 2).

Question 28.

12d + 6e + 18

Answer:

12d + 6e + 18 = 6(2d + e + 3).

Explanation:

12d + 6e + 18 = 6(2d) + 6(e) + 6(3)

= 6(2d + e + 3).

Question 29.

3s – 9t – 15

Answer:

3s – 9t – 15 = 3(s – 3t – 5).

Explanation:

3s – 9t – 15 = 3(s) + 3(-3t) + 3(-5)

= 3(s – 3t – 5).

Question 30.

4a – 6b – 12

Answer:

4a – 6b – 12 = 2(2a – 3b – 6).

Explanation:

4a – 6b – 12 = 2(2a) + 2(-3b) + 2(-6)

= 2(2a – 3b – 6).

Question 31.

12a – 9b – 6

Answer:

12a – 9b – 6 = 3(4a – 3b – 2).

Explanation:

12a – 9b – 6 = 3(4a) + 3(-3b) + 3(-2)

= 3(4a – 3b – 2).

Question 32.

24g – 12h – 36

Answer:

24g – 12h – 36 = 6(4g – 2h – 6).

Explanation:

24g – 12h – 36 = 6(4g) + 6(-2h) + 6(-6)

= 6(4g – 2h – 6).

**Solve. Show your work.
**Question 33.

A rectangle has an area of (12m – 30n) square units. Its width is 6 units. Factor the expression for the area to find an expression for the length of the rectangle.

Answer:

Length of the rectangle = 2m – 5n units .

Explanation:

Given Area of rectangle = (12m – 30n) square units.

Width = 6 units.

Formula: Area of rectangle = Length × Width

=> (12m – 30n) square units = Length × 6units.

=> (12m – 30n) ÷ 6 = Length

=> [6(2m – 5n) ] ÷ 6 = Length

=> 2m – 5n units = Length.