Chapter 6: Q. 6.16 (page 571)

Factor by grouping:
a) $y^{2} + 4 y - 7 y - 28$
b) $42 m^{2} - 18 m - 35 m + 15$

Short Answer

Expert verified

a) The factored form is $(y + 4) (y - 7)$ .

b) The factored form is $(7 - 3 m) (6 m - 5)$ .

Step by step solution

Part (a) Step 1. Given Information

The given expression is $y^{2} + 4 y - 7 y - 28$ .

Part (a) Step 2. Rewrite the given expression

All four terms do not have the greatest common factor.
Factor the GCF, $y$ from the first 2 terms of the given expression.

$y (4 + y) - 7 y - 28$

Factor the GCF, $- 7$ from the last two terms of the obtained expression.

$y (y + 4) - 7 (y + 4)$

Factor out the common factor $y + 4$ in the obtained expression.

$y (y + 4) - 7 (y + 4) = (y + 4) (y - 7)$

Part (b) Step 1. Given Information

The given expression is $42 m^{2} - 18 m - 35 m + 15$ .

Part (b) Step 2. Rewrite the given expression

All four terms do not have the greatest common factor.
Factor the GCF, $6 m$ from the first 2 terms of the given expression.

$6 m (7 - 3 m) - 35 + 15$

Factor the GCF, localid="1644907252557" $- 5$ from the last two terms of the obtained expression.

$6 m (7 - 3 m) - 5 (7 - 3 m)$

Factor out the common factor $7 - 3 m$ in the obtained expression.

$6 m (7 - 3 m) - 5 (7 - 3 m) = (7 - 3 m) (6 m - 5)$

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Factor by grouping:
a) $y^{2} + 4 y - 7 y - 28$
b) $42 m^{2} - 18 m - 35 m + 15$

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Rewrite the given expression

Part (b) Step 1. Given Information

Part (b) Step 2. Rewrite the given expression

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Factor by grouping:a)y2+4y-7y-28b)42m2-18m-35m+15

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Rewrite the given expression

Part (b) Step 1. Given Information

Part (b) Step 2. Rewrite the given expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Pure Maths

Discrete Mathematics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Factor by grouping:
a) $y^{2} + 4 y - 7 y - 28$
b) $42 m^{2} - 18 m - 35 m + 15$