Chapter 6: Q 173. (page 603)

In the following exercises, factor completely using the perfect square trinomial pattern.
$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$

Short Answer

Expert verified

The factor of the given trinomial is $3 u^{2} {(5 u - v)}^{2}$ .

Step by step solution

Step 1. Given information.

Consider the given trinomial.

$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$

Step 2. Factor out GCF

Factor out $3 u^{2}$ from the given trinomial.

$3 u^{2} (25 u^{2} - 10 u v + v^{2})$

Step 3. Find the factor of perfect square trinomial.

The middle term of the trinomial is negative, so the binomial square will be of the form ${(a - b)}^{2}$ .

$3 u^{2} [{(5 u)}^{2} - 2 \cdot 5 u \cdot v + {(v)}^{2}]$

Write factor

$3 u^{2} {(5 u - v)}^{2}$

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In the following exercises, factor completely using the perfect square trinomial pattern.
$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor out GCF

Step 3. Find the factor of perfect square trinomial.

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In the following exercises, factor completely using the perfect square trinomial pattern.75u4-30u3v+3u2v2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor out GCF

Step 3. Find the factor of perfect square trinomial.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Statistics

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, factor completely using the perfect square trinomial pattern.
$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$