factor and show steps.thanks: 20x^2 - 45y^2?

Answer 1

The first, and in my opinion most important rule of factoring is to factor out the greatest common factor, in this case, 5

5(4x^2-9y^2)

Now factor the difference of the two perfect squares.

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

Answer 2

First, find the greatest common factor of both terms

20x^2 and 45y^2 have a GCF of 5 so we are going to pull it out to the front and factor it from each term by dividing

20x^2 - 45y^2
5*(20x^2/5 - 45y^2/5)
5*(4x^2 - 9y2)

Now, the factor in the parenthesis is the difference of two perfect squares so it factors into the sum and difference of the square root of each like this

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

That's it

You can check by usingfoil and the distributive property to multiply you answer out and see if you get the original problem back.

Answer 3

Remember, always take out the common factor first. That's 5, and then the expression inside the parentheses is a difference of squares, which you can factorise as
a^2 - b^2 = (a + b)(a - b).

Hope you can do this yourself, but some other answerer probably will complete it for you (or already has); if not, contact me at

[e-mail]

Answer 4

1st factor out 5 to get 5(4x^2-9y^2)

This is of the form a^2-b^2 which can be factored
a^2-b^2=(a+b)(a-b).
here a=2x &
b=3y so
20x^2 - 45y^2=5(4x^2-9y^2)=5(2x+3y)(2x-3y)

Answer 5

20x^2 - 45y^2 = 5(4x^2 - 9y^2) = 5(2x - 3)(2x + 3)

Answer 6

= 5 * (4*x^2 - 9*y^2)
= 5 * (2x-3y) (2x+3y)

Answer 7

(2x-3y)*(10x+15y)