# Find the Value of the Following Expression: 16x2 + 24x + 9, When X = 7 4 - Mathematics

Find the value of the following expression: 16x2 + 24x + 9, when $x = \frac{7}{4}$

#### Solution

Let us consider the following expression: $16 x^2 + 24x + 9$

Now $16 x^2 + 24x + 9 = \left( 4x + 3 \right)^2$                (Using identity $\left( a + b \right)^2 = a^2 + 2ab + b^2$)

$\Rightarrow 16 x^2 + 24x + 9 = \left( 4 \times \frac{7}{4} + 3 \right)^2 (\text { Substituting } x = \frac{7}{4})$

$\Rightarrow 16 x^2 + 24x + 9 = \left( 7 + 3 \right)^2$

$\Rightarrow 16 x^2 + 24x + 9 = {10}^2$

$\Rightarrow 16 x^2 + 24x + 9 = 100$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 13.1 | Page 44