Question

a^4 + b^4 - 7a^2 b^2
Factorise it

Answer 1

Answer:

Step-by-step explanation:

a^4+b^4-7\,a^2b^2

=(a^2)^2+(b^2)^2-7\,a^2b^2

{Using the following identity}

(x+y)^2=x^2+y^2+2xy

x^2+y^2=(x+y)^2-2xy}

=(a^2+b^2)^2-2\,a^2b^2-7\,a^2b^2

=(a^2+b^2)^2-9\,a^2b^2

=(a^2+b^2)^2-(3\,ab)^2

{Using the following identity}

x^2-y^2=(x+y)(x-y)}

=(a^2+b^2+3ab)(a^2+b^2-3ab)

a^4+b^4-7,a^2b^2=(a^2+b^2+3ab)(a^2+b^2-3ab)}

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Answer 2

Answer:

a

$(a^2 + b^2 - 3ab)(a^2 + b^2 + 3ab)$