76) A4 + b4 - 7a2b2 factorise – InterviewSolution

1.	76) A4 + b4 - 7a2b2 factorise
Answer» $\textbf{Given:}$ $a^4+b^4-7\,a^2b^2$ $\textbf{To <klux>FIND</klux>:}$ $\text{Factors of $a^4+b^4-7\,a^2b^2$}$ $\textbf{Solution:}$ $\text{Consider,}$ $=(a^2)^2+(b^2)^2-7\,a^2b^2$ $\text{Using the following identity}$ $\boxed{\bf(x+y)^2=x^2+y^2+2xy\implies\,x^2+y^2=(x+y)^2-2xy}$ $=(a^2+b^2)^2-2\,a^2b^2-7\,a^2b^2$ $=(a^2+b^2)^2-9\,a^2b^2$ $=(a^2+b^2)^2-(3\,ab)^2$ $\text{Using the following identity}$ $\boxed{\bf\,x^2-y^2=(x+y)(x-y)}$ $=(a^2+b^2+3ab)(a^2+b^2-3ab)$ $\therefore\boxed{\bf\,a^4+b^4-7\,a^2b^2=(a^2+b^2+3ab)(a^2+b^2-3ab)}$ Find more: 1.X2-(a-1/a)x+1 FACTORISE the following brainly.in/question/4301404# 2.Factorise x^4-(x-z)^4 brainly.in/question/14993176