Question

a, 2x² - 4xy + 2y²       

b, x² + 4xy + 4y²  - 9 

c, x⁴ - x³y + x - y 

Answer 1

\(2x^2-4xy+2y^2\\ =2\left(x^2-2xy+y^2\right)\\ =2\left(x-y\right)^2\)

Answer 2

a) 2x²-4xy+2y²
= 2x²-2xy-2xy+2y²
= 2x(x-y)-2y(x-y)
= (2x-2y)(x-y)
b) x²+4xy+4y²-9
= (x+2y)²-3²
= (x+2y-3)(x+2y+3)
c) x⁴-x³y+x-y
= x³(x-y)+(x-y)
= (x³+1)(x-y)

Answer 3

\(a,=2\left(x^2-2xy+y^2\right)=2\left(x-y\right)^2\\ b,=\left(x+2y\right)^2-9=\left(x+2y-3\right)\left(x+2y+3\right)\\ c,=x^3\left(x-y\right)+\left(x-y\right)\\ =\left(x+1\right)\left(x-y\right)\left(x^2-x+1\right)\)