GCF(Greatest Common Factor) and Factor by Grouping.

Question

Factor:

4x(8x+6y)+2(8x+6y) =

Answer 1

Multiply out:

4x(8x+6y)+2(8x+6y) = 32x² + 24xy + 16x + 12y

= 32x² + 16x + 24xy + 12y

Factor out the greatest common factor of the first pair of terms and the last pair of terms:

= 16x ( 2x + 1) + 12 y ( 2x + 1 )

Factor out 2x + 1

= ( 16x + 12 y ) ( 2x+ 1 )

Factor out the greatest common factor of the first term:

= 4 ( 4x + 3y ) ( 2x + 1)

No additional factoring is possible. Check by multiplying out. (FOIL)

= 32x² + 24yx + 16x + 12y

= 32x² + 24xy + 16x + 12y

AND that is equivalent to our initial expression.

Answer 2

(4x+2)(8x+6y)

=4(2x+1)(4x+3)

4x(8x+6y)+2(8x+6y)

let z=8x+6y

then 4x(z)+2z = (4x+2)z = (4x+2)(8x+y)

that's called factor by grouping

=(4x+2)(8x+6y)

then factor a 2 out of each of those factors

=2(2x+1)(2)(4x+3)

multiply the 2 two's together to get 4

= 4(2x+1)(4x+3)