Chapter 6: Q 6.52 (page 595)

Factor: $27 p^{2} q + 90 p q + 75 q$ .

Short Answer

Expert verified

Factors of $27 p^{2} q + 90 p q + 75 q$ are $3 q {(3 p + 5)}^{2}$ .

Step by step solution

Step 1. Given information.

Given an expression $27 p^{2} q + 90 p q + 75 q$ .

Step 2. Find if GCF of all the three terms.

GCD stands for greatest common factor.

Here, $3 q$ is GCF of $27 p^{2} q + 90 p q + 75 q$ .

So, the expression can be written as $3 q (9 p^{2} + 30 p + 25)$ .

Step 3. Find if it is a perfect trinomial.

A perfect trinomial is of the form $a^{2} \pm 2 a b + b^{2}$ ..

Consider $a = 3 p, b = 5$ .

Following result can be obtained.

$\begin{array}{rcl} 3 q (9 p^{2} + 30 p + 25) & = & 3 q ({(3 q)}^{2} + 2 (3 p) (5) + 5^{2}) \\ = & 3 q (a^{2} + 2 a b + b^{2}) \end{array}$

Therefore, the expression is a perfect trinomial and can be expressed as $3 q {(3 p + 5)}^{2}$ .

Step 4. Verify the result.

Multiply the factors as follows.

$\begin{array}{rcl} 3 q {(3 p + 5)}^{2} & = & 3 q ({(3 p)}^{2} + 2 (3 p) (5) + 5^{2}) \\ = & 3 q (9 p^{2} + 30 p + 25) \\ = & 27 p^{2} q + 90 p q + 75 q \end{array}$

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Factor: $27 p^{2} q + 90 p q + 75 q$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if GCF of all the three terms.

Step 3. Find if it is a perfect trinomial.

Step 4. Verify the result.

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Factor:27p2q+90pq+75q.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if GCF of all the three terms.

Step 3. Find if it is a perfect trinomial.

Step 4. Verify the result.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Factor: $27 p^{2} q + 90 p q + 75 q$ .