Factor each given by grouping

Question

Factoring by grouping:

1. x²+2xy-z²+y²=

2. xy+2x-y-2=

3. ab+ac+bt+cd=

4. t²+4st+4s²-16g²=

5. 20+5x+8y+2xy=

Answer 1

x^2 +2xy -z^2 + y^2

= (x^2 + 2xy + y^2) -z^2

= (x+y)^2 -z^2

=(x+y+z)(x+y-z)

xy+2x -y-2

= 2x-2 +xy-y

= 2(x-1) +y(x-1)

=(2+y)(x-1)

t^2+4st+t^2 -16g^2

=(t+t)^2 - 16g^2

= (t+s+4g)(t+s-4g)

20+5x +8y +2xy

=5(4+x) +2y(4+x)

=(5+2y)(4+x)

ab+ac +bd +cd

=a(b+c) + d(b+c)

=(a+d)(b+c)