The correct option is B (a 1)(a+1)(a^2+1)a^4 1 We know a^2 b^2 = (a+b)(a b) a^4 1 = (a^2)^2 (1^2)^2 Let a^2 = k (a^2)^2 1 = k^2 1= (k+1)(k 1) (k+1) ...

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Standard XII

Chemistry

Heat Capacity

Factorise a4-...

Question

Factorise $a^{4} - 1$ is ____

(a - 1) (a + 1) (a^{2} + 1)

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(a^{2} - 1) (a + 1) (a^{2} + 1)

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(a^{2} - 1) (a^{2} + 2) (a^{2} + 1)

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(a + 11) (2 a + 1) (a^{2} - 1)

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Solution

The correct option is A $(a - 1) (a + 1) (a^{2} + 1)$
$a^{4} - 1$
We know $a^{2} - b^{2} = (a + b) (a - b)$
$a^{4} - 1 = (a^{2})^{2} - (1^{2})^{2}$
Let $a^{2} = k$
$(a^{2})^{2} - 1 = k^{2} - 1 = (k + 1) (k - 1)$
$(k + 1) (k - 1) = (a^{2} + 1) (a^{2} - 1)$
Factorising further , we get
$(a^{2} + 1) (a^{2} - 1) = (a^{2} + 1) (a - 1) (a + 1)$

Suggest Corrections

Factorise a4−1 is ____

The correct option is A (a−1)(a+1)(a2+1)a4−1 We know a2−b2=(a+b)(a−b) a4−1=(a2)2−(12)2 Let a2=k (a2)2−1=k2−1=(k+1)(k−1) (k+1)(k−1)=(a2+1)(a2−1) Factorising further , we get (a2+1)(a2−1)=(a2+1)(a−1)(a+1)

Factorise $a^{4} - 1$ is ____