Completely factor the expression
20x2 – 45y2
45 is not a perfect aquare , sadly
5 ( 4 x^2 - 9 y^2) ah, now we are talking
5 (2x-3y)(2x+3y)
To completely factor the expression 20x^2 - 45y^2, we first look for the greatest common factor (GCF) of the two terms.
Step 1: Find the GCF
The GCF of 20x^2 and 45y^2 can be determined by finding the common factors of the coefficients (20 and 45) and the variables (x^2 and y^2).
The prime factors of 20 are 2^2 * 5, and the prime factors of 45 are 3^2 * 5.
The common factor is 5.
The largest power of x that divides both 20x^2 and 45y^2 is x^0 = 1.
The largest power of y that divides both 20x^2 and 45y^2 is y^0 = 1.
So, the GCF is 5xy.
Step 2: Divide by the GCF
We divide the expression 20x^2 - 45y^2 by the GCF (5xy).
20x^2 - 45y^2 = 5xy(4x - 9y)(4x + 9y)
Step 3: Write the Factored Form
The completely factored form of the expression 20x^2 - 45y^2 is 5xy(4x - 9y)(4x + 9y).