Chapter 11: Q 52E (page 1069)

In the following exercises, factor.
$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ .

Short Answer

Expert verified

The obtained factor for the expression $- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ is, $- x y^{3} (4 x^{2} y^{2} + x - 12 y)$ .

Step by step solution

Given expression is,

$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ .

The objective is, we need to find the factor for this expression.

Step 2 First find the GCF for the given expression.

$- 4 x^{3} y^{5} = - 2 \times 2 \times x \times x \times x \times y \times y \times y \times y \times y - x^{2} y^{3} = - 1 \times x \times x \times y \times y \times y 12 x y^{4} = 2 \times 6 \times x \times y \times y \times y \times y$

The GCF is, $x y^{3}$ .

In the given expression, rewrite the each term using GCF.

$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4} = x y^{3} (- 4 x^{2} y^{2}) + x y^{3} (- x) + x y^{3} (12 y)$

Now factor out the GCF.

$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4} = x y^{3} (- 4 x^{2} y^{2} - x + 12 y) = - x y^{3} (4 x^{2} y^{2} + x - 12 y)$

The obtained factor is, $- x y^{3} (4 x^{2} y^{2} + x - 12 y)$

Step 4 Let us check the answer by multiplying the factors.

$- x y^{3} (4 x^{2} y^{2} + x - 12 y) = - 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$

which is true.

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In the following exercises, factor.
$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ .

Short Answer

Step by step solution

Given expression is,

Step 2 First find the GCF for the given expression.

In the given expression, rewrite the each term using GCF.

Step 4 Let us check the answer by multiplying the factors.

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In the following exercises, factor.−4x3y5−x2y3+12xy4.

Short Answer

Step by step solution

Given expression is,

Step 2 First find the GCF for the given expression.

In the given expression, rewrite the each term using GCF.

Step 4 Let us check the answer by multiplying the factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor.
$- 4 x^{3} y^{5} - x^{2} y^{3} + 12 x y^{4}$ .