Question

Factorise : x 4 + y 4 - 18x 2y 2 .​

Answer 1

Solution :

Here we have to factorise :

x⁴ + y⁴ - 18 x²y²

>> (x²)² + (y²)² - 18x²y²

>> (x²)² + (y²)² - 2x²y² - 16 x²y²

>> (x²-y²)² - 16x²y²

>> (x²-y²)² - (4xy)²

>> (x²-4xy-y²)(x²+4xy-y²)

This is the required answer.

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

Answer 2

Answer:

x4-y4-11x2y2

=x4-2x2y2+y4-9x2y2

=(x2-y2)2-(3xy)2

=(x2-3xy-y2) (X2+3xy-y2) is answer