Question

Answer 1

a) \(5x^2+10xy+5y^2=5\left(x^2+2xy+y^2\right)=5\left(x+y\right)^2\)

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

c) \(x^2+3x-xy-3y=x\left(x+3\right)-y\left(x+3\right)=\left(x-y\right)\left(x+3\right)\)

d) \(a^2-4+4b-b^2=a^2-\left(4-4b+b^2\right)=a^2-\left(2-b\right)^2=\left(a-2+b\right)\left(a+2-b\right)\)

Answer 2

a) \(=5\left(x^2+2xy+y^2\right)=5\left(x+y\right)^2\)

b) \(=\left(x-y\right)\left(x+y\right)+4\left(x-y\right)=\left(x-y\right)\left(x+y+4\right)\)

c) \(=x\left(x+3\right)-y\left(x+3\right)=\left(x+3\right)\left(x-y\right)\)

d) \(=a^2-\left(b^2-4b+4\right)=a^2-\left(b-2\right)^2\)

\(=\left(a-b+2\right)\left(a+b-2\right)\)

Answer 3

Bài 2:

a)5x²+10xy+5y²=5(x²+2xy+y²)=5(x+y)²

b)x²-y²+4x-4y=(x+y)(x-y)+4(x-y)=(x-y)[(x+y)+4]=(x-y)(x+y+4)

c)x²+3x-xy-3y=(x²+3x)-(xy+3y)=x(x+3)-y(x+3)=(x+3)(x-y)

d)a²-4+4b-b²=a²-(b²-4b+4)=a²-(b²-4b+2²)=a²-(b-2)²=[a+(b-2)][a-(b-2)]=(a+b-2)(a-b+2)