Chapter 6: Q. 387 (page 635)

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

Short Answer

Expert verified

The factorisation of the given polynomial is:

$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 3 u^{2} {(5 u - v)}^{2}$

Step by step solution

Step 1. Given information

The given polynomial is:

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

Step 2. Factorise the polynomial

We know that,

${(a + b)}^{2} = a^{2} - 2 a b + b^{2}$

For the polynomial $75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$ , taking out $3 u^{2}$ as a common, we get:

localid="1644657545562" $3 u^{2} (25 u^{2} - 10 u v + 3 v^{2})$

Now,

localid="1644657824561" $3 u^{2} (25 u^{2} - 10 u v + v^{2}) 3 u^{2} [{(5 u)}^{2} - 2 \times 5 u \times v + v^{2}] 3 u^{2} {(5 u - v)}^{2} [u \sin g {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$

The factorisation of the given polynomial is:

localid="1644657866268" $75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 3 u^{2} {(5 u - v)}^{2}$

Step 3. Check the answer

Multiplying the factors we get:

$75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 3 u^{2} {(5 u - v)}^{2} 75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 3 u^{2} (5 u - v) (5 u - v) 75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 3 u^{2} (25 u^{2} - 10 u v + v^{2}) 75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2} = 75 u^{4} - 30 u^{3} v + 3 u^{2} v^{2}$

This is true.

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In the following exercise, factor completely using the perfect square trinomials 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. Factorise the polynomial

Step 3. Check the answer

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Factorise the polynomial

Step 3. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Geometry

Pure Maths

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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