Chapter 8, Problem 20MCQ

To determine

To simplify the given expression $x\left(4x+5\right)+3\left(2x^2-4x+1\right)$ .

Answer to Problem 20MCQ

(B) $10x^2-7x+3$

Explanation of Solution

Given:

  $x\left(4x+5\right)+3\left(2x^2-4x+1\right)$

Formula used:

Distributive Law:

  $x\left(y\pm z\right)=x\cdot y\pm x\cdot z$

Calculation:

Consider the given expression,

  $\Rightarrow x\left(4x+5\right)+3\left(2x^2-4x+1\right)$

  $\Rightarrow x\cdot 4x+x\cdot 5+3\cdot 2x^2-3\cdot 4x+3\cdot 1$  [ $\because$$x\left(y\pm z\right)=x\cdot y\pm x\cdot z$ ]

  $\begin{array}{l}\Rightarrow 4x^2+5x+6x^2-12x+3\\ \Rightarrow 4x^2+6x^2+5x-12x+3\\ \Rightarrow 10x^2-7x+3\end{array}$

Conclusion:

Therefore, the simplification of the given expression is $10x^2-7x+3$ .

The correct option is (B).