Question

Factorise 100-(x-5)^2

Answer 1

Answer:

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firstly we take sq root of 100 that is 10².

then,

(10)²-(x–5)²

=5(10+x–5) 5(10–x+5)

=(5+x)(5–x)

Answer 2

Given:

100-(x-5)²

To find:

Factorized form of 100-(x-5)²

Solution:

The factorized form of 100-(x-5)² is (15-x)(5-x).

We can find the factors by following the steps given below-

We know that the given expression can be factorized by using the following formula-

a²-b²=(a-b)(a+b)

The given expression= 100-(x-5)²

It can also be written as 10²-(x-5)²

Using the aforementioned formula,

10²-(x-5)²=(10-(x-5)(10+(x-5))

On solving it, we get

=(10-x-(-5))(10+x-5)

=(10-x+5)(10-x-5)

=(15-x)(5-x)

On factorizing 100-(x-5)², we get (15-x)(5-x).

Therefore, the factorized form of 100-(x-5)² is (15-x)(5-x).