Chapter 6: Q 6.59 (page 598)

Factor: $x^{2} - 10 x + 25 - y^{2}$ .

Short Answer

Expert verified

Factors of $x^{2} - 10 x + 25 - y^{2}$ are $(x - 5 - y) (x - 5 + y)$ .

Step by step solution

Step 1. Given information.

Given an expression $x^{2} - 10 x + 25 - y^{2}$ .

Step 2. Factor by grouping the first 3 therms if it forms a perfect square trinomial.

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

First 3 terms of the expression are $x^{2} - 10 x + 25$ which can be expressed as ${(x)}^{2} - 2 (x) (5) + 5^{2}$ .

So, Factor by grouping as $x^{2} - 10 x + 25 = {(x - 5)}^{2}$ .

It follows that the expression has first 3 terms that forms a perfect square trinomial.

Step 3. Write them as square if it is a difference of square.

It can be seen that ${(x - 5)}^{2} - y^{2}$ is a difference of square.

Consider $a = x - 5$ and $b = y$ .

Step 4. Factor as products of conjugates.

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

Therefore, ${(x - 5)}^{2} - y^{2} = (x - 5 - y) (x - 5 + y)$ .

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Factor: $x^{2} - 10 x + 25 - y^{2}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor by grouping the first 3 therms if it forms a perfect square trinomial.

Step 3. Write them as square if it is a difference of square.

Step 4. Factor as products of conjugates.

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Factor:x2-10x+25-y2.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Factor by grouping the first 3 therms if it forms a perfect square trinomial.

Step 3. Write them as square if it is a difference of square.

Step 4. Factor as products of conjugates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Factor: $x^{2} - 10 x + 25 - y^{2}$ .