Q. 6.7

Question

Factor: $15 x^{3} y - 3 x^{2} y^{2} + 6 x y^{3}$

Step-by-Step Solution

Verified

Answer

The factored form is $\begin{array}{rcl} 3 x y (5 x^{2} - x y + 2 y^{2}) \end{array}$ .

1Step 1. Given Information

The given expression is $15 x^{3} y - 3 x^{2} y^{2} + 6 x y^{3}$ .

2Step 2. Find GCF of the terms

Factor each of the terms in the given expression.

$15 x^{3} y = 3 \cdot 5 \cdot x \cdot x \cdot x \cdot y 3 x^{2} y^{2} = 3 \cdot x \cdot x \cdot y \cdot y 6 x y^{3} = 2 \cdot 3 \cdot x \cdot y \cdot y \cdot y$

From the obtained factors, it is observed that the common factors are $3, x, y$ .
Multiply the common factors to determine the GCF of the terms of the given expression.

$3 \cdot x \cdot y = 3 x y$

So, the GCF of the terms of the given expression is $3 x y$ .

3Step 3. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $3 x y$ .

$3 x y \cdot 5 x^{2} - 3 x y \cdot x y + 3 x y \cdot 2 y^{2}$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

$3 x y \cdot 5 x^{2} - 3 x y \cdot x y + 3 x y \cdot 2 y^{2} = 3 x y (5 x^{2} - x y + 2 y^{2})$

4Step 4. Check

Multiply the obtained factors.

$\begin{array}{rcl} 3 x y (5 x^{2} - x y + 2 y^{2}) & = & 3 x y \cdot 5 x^{2} - 3 x y \cdot x y + 3 x y \cdot 2 y^{2} \\ = & 15 x^{3} y - 9 x^{2} y^{2} + 6 x y^{3} \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

Q. 6.6

Q. 6.8

Other exercises in this chapter

Factor: 8a3b+2a2b2-6ab3.