Question

from the chapter
FACTORIZATION OF THE ALGEBRAIC EXPRESSION


factorize the following using identities
$(v) {a}^{4} - 10 {a}^{2} {b}^{2} + 25 {b}^{4}$


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Answer 1

factorize an algebraic expression easily.

The following identities are:

(i) (a + b)2 = a2 + 2ab +b2,

(ii) (a - b)2 = a2 - 2ab + b2 and

(iii) a2 – b2 = (a + b)(a – b).

Answer 2

Required Answer:-

Question:

• Factorise a⁴ - 10a²b² + 25b⁴

Solution:

As we know that,

(a - b)² = a² - 2ab + b²

Here, the given polynomial can be expressed in (a - b)² form. We will do that.

Therefore,

a⁴ - 10a²b² + 25b⁴

= (a²)² - 2 × a² × 5b² + (5b²)²

= (a² - 5b²)² [Applying the identity]

Now, it can't be factorised more.

Hence, the factorised form of the given polynomial is (a² - 5b²)².

Answer:

• Factorised form is (a² - 5b²)²

Identity Used:

• (a - b)² = a² - 2ab + b²