Question

Square of a trinomial/polynomial
4x^+9y^2+4+8x-12y-12xy

Answer 1

Answer:

4x

2

+12xy+9y

2

−8x−12y

consider

4x

2

+12xy+9y

2

4x

2

+6xy+6xy+9y

2

2x(2x+3y)+3y(2x+3y)

(2x+3y)(2x+3y)

let

4x

2

+12xy+9y

2

−8x−12y=(2x+3y+l)(2x+3y+m)

4x

2

+12xy+9y

2

−8x−12y=4x

2

+12xy+9y

2

+(2m+2l)x+(3m+3l)y+lm

oncomparison

2m+2l=−8

m+l=−4

3m+3l=−12

m+l=−4

ml=0

eitherm=0orl=0

thentheotheris−4

Therefore

4x

2

+12xy+9y

2

−8x−12y=(2x+3y)(2x+3y−4)