Question

(a^2 + 1) b^2 - b^4 - a^2: factorise

hey, plz solve my question fastttt
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Answer 1

Solution :-

(a² + 1)b² - b⁴ - a²

= a²b² + b² - b⁴ - a²

Rearranging the terms we get,

= a²b² - b⁴ - a² + b²

It can be written as :

= a²b² - b²b² - a² + b²

Taking b² common we get,

= b²(a² - b²) - a² + b²

= b²(a² - b²) - 1(a² - b²)

= (b² - 1)(a² - b²)

= (b² - 1²)(a² - b²)

Expanding the terms using identity : x² - y² = (x + y)(x - y)

= (b + 1)(b - 1)(a + b)(a - b)

Therefore (b + 1)(b - 1)(a + b)(a - b) are the factors of (a² + 1)b² - b⁴ - a².

Answer 2

Question :-

Factories it :

→ (a² + 1)b² - b⁴ - a²

Answer :-

→ ( a - b)(a + b)(b +1)(b - 1)

Explanation :-

We have ,

→ (a² + 1)b² - b⁴ - a²

→ a² b² + b² - b⁴ - a²

→ a² b² - b⁴ + b² - a²

→b² ( a² - b² ) -( - b² + a²)

→ b²(a² - b²)-(a² - b²)

→ (a² - b²)(b² - 1)

we can write it ,

→ ( a - b)(a + b)(b +1)(b - 1)

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Hope it will help you : )