Factor the following expression completely:
45x^3y – 80xy
45X^3Y - 80XY.
5XY(9X^2 - 16).
To factor the expression 45x^3y - 80xy completely, we can first find the greatest common factor (GCF) of the terms.
Step 1: Find the GCF
The GCF of 45x^3y and 80xy is 5xy.
Step 2: Divide each term by the GCF
Dividing 45x^3y by 5xy, we get 9x^2.
Dividing 80xy by 5xy, we get 16.
Now the expression becomes:
5xy(9x^2 - 16)
Step 3: Check for further factoring
The expression 9x^2 - 16 is a difference of squares, which can be factored further using the formula (a^2 - b^2) = (a + b)(a - b).
In this case, a = 3x and b = 4.
So, we have:
5xy(3x + 4)(3x - 4)
Therefore, the expression 45x^3y - 80xy can be factored completely as:
5xy(3x + 4)(3x - 4)