Question

Factorise `x²+7xy+12y²` ?

Answer 1

See the answer below...

Explanation:

`x^2+7xy+12y^2`

`=x^2+3xy+4xy+12y^2" "`

`=x(x+3y)+4y(x+3y)`

`=color(red)(ul(bar(|color(green)((x+3y)(x+4y))|`

[It is called middle term factor process of factorization.]

Here, you have to break the middle factor in such a way that the the product of the formers will be equal to the products of the co-efficient of the first and last term with sign.

Hope it helps...

Thank you...

:-)

Answer 2

`(x+3y)(x+4y)`

Explanation:

`"this can be factored in the same way as a quadratic"`
`"in one variable"`

`"the factors of + 12 which sum to + 7 are + 3 and + 4"`

`rArrx^2+7xy+12y^2=(x+3y)(x+4y)`