Chapter 6: Q 6.50 (page 595)

Factor: $64 m^{2} + 112 m n + 49 n^{2}$ .

Short Answer

Expert verified

Factors of $64 m^{2} + 112 m n + 49 n^{2}$ is ${(8 m + 7 n)}^{2}$ .

Step by step solution

Step 1. Given information.

Given an expression $64 m^{2} + 112 m n + 49 n^{2}$ .

Step 2. Find if first and last term are perfect squares or not.

First term is $64 m^{2}$ which can be expressed as ${(8 m)}^{2}$ .

Last term is $49 n^{2}$ which can be expressed as ${(7 n)}^{2}$ .

Consider $a = 8 m$ and $b = 7 n$ .

So, first and last term are perfect squares.

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

Here, middle term is $112 m n$ which can be expressed as $2 \times 8 m \times 7 n$ .

It follows that middle term is of the form .

Step 4. Write the square of the binomial.

So, $64 m^{2} + 112 m n + 49 n^{2}$ is a perfect square trinomial of the form $a^{2} + 2 a b + b^{2}$ .

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

Therefore, $64 m^{2} + 112 m n + 49 n^{2} = {(8 m + 7 n)}^{2}$ .

Step 5. Check by multiplying.

Verification can be obtained as follows.

$\begin{array}{rcl} {(8 m + 7 n)}^{2} & = & {(8 m)}^{2} + 2 \times 8 m \times 7 n + {(7 n)}^{2} \\ = & 64 m^{2} + 112 m n + 49 n^{2} \end{array}$

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Factor: $64 m^{2} + 112 m n + 49 n^{2}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if first and last term are perfect squares or not.

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

Step 4. Write the square of the binomial.

Step 5. Check by multiplying.

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Factor:64m2+112mn+49n2.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find if first and last term are perfect squares or not.

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

Step 4. Write the square of the binomial.

Step 5. Check by multiplying.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Factor: $64 m^{2} + 112 m n + 49 n^{2}$ .