Chapter 6: Q. 159 (page 603)

Factor $16 y^{2} + 24 y + 9$ completely using the perfect square trinomials pattern.

Short Answer

Expert verified

Factors of $16 y^{2} + 24 y + 9$ are ${(4 y + 3)}^{2}$ .

Step by step solution

Step 1. Given information.

Given an expression $16 y^{2} + 24 y + 9$ .

Step 2. Check if the first and last term of the expression a perfect square.

First term and last term are $16 y^{2}$ and 9 respectively.

Consider $a = 4 y$ and $b = 3$ .

It can be seen that $16 y^{2} = {(4 y)}^{2}$ and $9 = 3^{2}$ .

Therefore, first and last terms are perfect squares.

Step 3. Check is the middle term of the form ±2ab.

Middle term of the expression is $24 y$ .

Also, $24 y = 2 (4 y) (3)$ .

It folllows that middle term is of the form $2 a b$ .

Step 4. Write the square of the binomial.

Note that ${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ .

Obtain the result as follows.

$\begin{array}{rcl} 16 y^{2} + 24 y + 9 & = & {(4 y)}^{2} + 2 (4 y) (3) + 3^{2} \\ = & {(4 y + 3)}^{2} \end{array}$

Step 5. Check the result.

Verify the result as follows.

$\begin{array}{rcl} {(4 y + 3)}^{2} & = & {(4 y)}^{2} + 2 (4 y) 3 + 3^{2} \\ = & 16 y^{2} + 24 y + 9 \end{array}$

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Factor $16 y^{2} + 24 y + 9$ completely using the perfect square trinomials pattern.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check if the first and last term of the expression a perfect square.

Step 3. Check is the middle term of the form ±2ab.

Step 4. Write the square of the binomial.

Step 5. Check the result.

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Factor 16y2+24y+9completely using the perfect square trinomials pattern.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Check if the first and last term of the expression a perfect square.

Step 3. Check is the middle term of the form ±2ab.

Step 4. Write the square of the binomial.

Step 5. Check the result.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Factor $16 y^{2} + 24 y + 9$ completely using the perfect square trinomials pattern.