Question

7. Factorise:

$a {}^{4} + 4$


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Answer 1

Siso , in third line , I have added and subtracted same value. Consequently , the value haven't changed !!

Don't go on handwriting

Answer 2

Answer:

Step-by-step explanation:

let me tell you first one another formula you have to remember :

4a^2b^2=(a^2+b^2)^2 —(a^2-b^2);

now coming to the question we get by simplification :

a^4+b^4=(a^2)^2+(b^2)^2;

=(a^2+b^2)^2–2a^2b^2;

=(a^2+b^2)^2—(1/2)[4a^2b^2];

now applying the upper mentioned simplification :

=(a^2+b^2)^2—(1/2)[(a^2+b^2)^2—(a^2-b^2)^2];

=(1/2){(a^2+b^2)^2+(a^2-b^2 )^2};

another one :

a^4+b^4=(a^2)^2+(b^2)^2;

=(a^2+b^2)^2–2a^2b^2;

=(a^2+b^2)^2—(√ 2ab)^2;

=(a^2+√ 2ab+b^2)(a^2-√ 2ab+b^2);