Q 264

In the following exercises, factor completely.

$60 x^{2} y - 75 x y + 30 y$

Verified

Answer

The expression is factored as $60 x^{2} y - 75 x y + 30 y = 15 y (4 x^{2} - 5 x + 2)$

1Step 1. Given Information

Consider the expression $60 x^{2} y - 75 x y + 30 y$

We need to factor the expression completely.

2Step 2. Factor out the GCF

The GCF of the three terms in the expression is $15 y$ . So factor the GCF from the expression we get

\begin{array}{rcl} 60 x^{2} y - 75 x y + 30 y & = & 15 y \cdot 4 x^{2} - 15 y \cdot 5 x + 15 y \cdot 2 \\ = & 15 y (4 x^{2} - 5 x + 2) \end{array}

The trinomial is prime and it cannot be factored more.

3Step 3. Check the solution

Multiply the factors to check the solution

$15 y (4 x^{2} - 5 x + 2) = 15 y \cdot 4 x^{2} - 15 y \cdot 5 x + 15 y \cdot 2 = 60 x^{2} y - 75 x y + 30 y$

And we get the given expression. So the expression is correctly factored.