Question

Factor 9y^2-12y+4


(3y-2)^2
(3y-2)(3y+2)
(3y-4)(y+1)

Answer 1

Choice a is correct answer.

Explanation:

Given expression is:

9y²-12y+4

We have to find its factor.

Split the middle term of above expression so that their sum should be -12 and their product should be 36.

9y²-6y-6y+4

Making two groups and taking common,we get

3y(3y-2)-2(3y-2)

Taking (3y-2) as common,we get

(3y-2)(3y-2)

(3y-2)² which is the answer.

Answer 2

(3y-2)^2

Explanation:

To factor the polynomial, find the binomials which multiply to make it. This can be done for any polynomial
`ax^2+bx+c` by finding numbers that multiply to a*c and add to b.

a*c=36 b=-12

36: 1, 2, 3, 4, 6. 6. 9, 12, 18, 36

Since -6*-6 = 36 and -6 + -6 = -12, split -12y in
`9y^2-12y+4` to
`9y^2-6y-6y+4`.

Next, factor by grouping by finding GCF between pairs of terms:

`(9y^2-6y)+(-6y+4)\\3y(3y-2)-2(3y-2)\\(3y-2)(3y-2)\\(3y-2)^2`

(3y-2)^2 is the solution.