Answer:
[tex](x - 2y)((x - 2y) - 4) + 4[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 4xy - 4x + 4y^2 + 8y + 4[/tex]
Required
Factorize
[tex]x^2 - 4xy - 4x + 4y^2 + 8y + 4[/tex]
Rearrange
[tex]x^2 - 4xy + 4y^2- 4x + 8y + 4[/tex]
Group into three
[tex](x^2 - 4xy + 4y^2)- (4x - 8y) + (4)[/tex]
Factorize the first bracket
[tex](x^2 - 2xy- 2xy + 4y^2) - (4x - 8y) + (4)[/tex]
[tex]x(x - 2y) - 2y(x - 2y)- (4x - 8y) + (4)[/tex]
[tex](x - 2y)(x - 2y) - (4x - 8y) + (4)[/tex]
Factorize the second bracket
[tex](x - 2y)(x - 2y) - 4(x - 2y) + 4[/tex]
x - 2y is a common factor of [tex](x - 2y)(x - 2y) - 4(x - 2y)[/tex]
So, the expression becomes
[tex](x - 2y)((x - 2y) - 4) + 4[/tex]
The expression cannot be further simplified;
Hence, [tex]x^2 - 4xy - 4x + 4y^2 + 8y + 4[/tex] is equivalent to [tex](x - 2y)((x - 2y) - 4) + 4[/tex]
