Factor completley and show the work 9x^2 + 12xy + 4y^2 - 25?

Question

9x^2 + 12xy + 4y^2 - 25

Answer 1

Let us keep the polynomials of 2nd order together and constant spearate
= (9x^2+12xy+4y^2) - 25
factorization of polynomial
we realize the polynomial to be a perferct square = (3x+2y)^2
so we put expression as (3x+2y)^2- 5^2 to get into a^2-b^2 form which is (a+b)(a-b)
using the above we get

(3x+2y+5)(3x+2y-5)

Answer 2

let us collect the constants and the ones with the powers seperately.

(9x^2 + 12xy + 4y^2) - 25

if you see the first bit in the bracket, its a whole square of
(3x + 2y) = (3x)^2 + 2(3x)(2y) + (2y)^2
= 9x^2 + 12xy + 4y^2

We can thus say that:
(3x + 2y)^2 - 25
= (3x + 2y)^ 2 - (5)^2

According to the following
(a - b)^2 = (a + b) (a - b)

we can say that: (3x+2y) is like 'a' and 5 is like 'b'

thus,
[ (3x + 2y) + 5 ] [ (3x + 2y) - 5 ]

this is the answer.

Hope you undestood how to solve this question and will not get stuck again on such questions. Best of luck though.

Answer 3

(9x^2 + 12xy + 4y^2) - 25 = (3x + 2y)^2 - 5^2
= (3x + 2y + 5)(3x +2y - 5)

Answer 4

9x^2 + 12xy + 4y^2 - 25
[(3x)^2 + 2(3x)(2y) + (2y)^2] - (5)^2
(3x + 2y)^2 - (5)^2
(3x + 2y -5) (3x + 2y +5)
hope u understood boss.