b) \(4x^4-12x^2y+9y^6=\left(2x^2-3y^3\right)^2\)
c) \(36x^2-25\left(x-y\right)^2=\left(6x-5x+5y\right)\left(6x+5x-5y\right)=\left(x+5y\right)\left(11x-5y\right)\)
d) \(\left(x^2+1\right)^2-4x^2=\left(x^2+1-2x\right)\left(x^2+1+2x\right)=\left(x-1\right)^2\left(x+1\right)^2\)
b: \(4x^4-12x^2y^3+9y^6=\left(2x^2-3y^3\right)^2\)
c: \(36x^2-25\left(x-y\right)^2\)
\(=36x^2-\left(5x-5y\right)^2\)
\(=\left(6x-5x+5y\right)\left(6x+5x-5y\right)\)
\(=\left(x+5y\right)\left(11x-5y\right)\)
d: \(\left(x^2+1\right)^2-4x^2\)
\(=\left(x^2+2x+1\right)\left(x^2-2x+1\right)\)
\(=\left(x+1\right)^2\cdot\left(x-1\right)^2\)
b. 4x4 - 12x2y3 + 9y6
= (2x2)2 - 12x2y3 + (3y3)2
= (2x2 - 3y3)2
d. (x2 + 1)2 - 4x2
= (x2 + 1)2 - (2x)2
= (x2 + 1 - 2x)(x2 + 1 + 2x)
= (x2 - 2x + 1)(x2 + 2x + 1)
= (x2 - x - x + 1)(x2 + x + x + 1)
= \(\left[x\left(x-1\right)-\left(x-1\right)\right]\left[x\left(x+1\right)+\left(x+1\right)\right]\)
= (x - 1)(x - 1)(x + 1)(x + 1)
= (x - 1)2 . (x + 1)2
