some help please?

Question

Factor the polynomial.

4 y^2 - 25

Still having problems understanding how to get the answer, can anyone tell me step by step please

Answer 1

(2y - 5)(2y +5)

To begin with, we know that 4 is just 2*2, and 25 is 5*5, so that's a start to get 4 and 25 in the equation. Next, since it's -25, one of the 5 has to be negative and one of the 5 has to be positive because negative * positive = negative, so that gives 5 and -5. We also know that y * y is y^2. So 2y * 2y gives 4y*y. So just factor them out, (2y + 5)(2y - 5).

Answer 2

Ok first there is only two ways to make 4, 4 x 1 (4y x y) or 2 x 2 (2y x 2y) so you know it is either (4y - 5)(y+5) or (2y-5)(2y + 5) since it is a minus polynomial there has to be a + and a - when you factor it. As for the 25 it is either 25 x 1 or 5 x 5. It has to be two number that cancel each other.

4y2-25 = (2y +5)(2y-5)

Answer 3

Compare it to the following equation:
(a + b)(a - b) = a^2 - ab + ab - b^2 = a^2 - b^2
4 is a square, y^2 is a square, and 25 is a square, so you can rewrite the polynomial as
(2y)^2 - 5^2
substituting 2y for a and 5 for b, you find the factors are
(2y + 5)(2y - 5)

Answer 4

Alright for starters, notice that each number and term is a perfect square of something...
Such as...

4 is 2^2
y is y^2
25 is 5^2

So with that knowledge and the knowledge that this is a "special" polynomial (one of the ones that looks like "(a^2)(y^2) - (b^2) ) you're set...

This polynomial is going to look like (when it's factored)
(ay + b) (ay - b)

As stated above, we already know what a and b are...
a = 2 (because 2^2 = 4)
b = 5 (because 5^2 = 25)

So just plug in the numbers for the variables...

(ay + b) (ay - b)
=
(2y + 5) (2y - 5)

Hope it helps!