Question

Simplify the expression: $5+7x\left[3\right(4x+9)+8]$

• A. $x^2+245x+5$
• B. $84x^2+245x$
• C. $84x^2+250x$
• D. $84x^2+245x+5$

Answer 1

The correct option is D $84x^2+245x+5$

$\underset{–}{\text{Need to Simplify:}}5+7x\left[3\right(4x+9)+8]$

$\underset{–}{\text{Step 1:}}$
First, we would solve the square bracket:
$5+7x\left[3\right(4x+9)+8]$

$=5+7x[3\times (4x)+3\times (9)+8]$

$=5+7x\left[\right(12x+27)+8]$

$=5+7x[12x+27+8]$

Now, adding the like terms inside the square bracket:

$=5+7x[12x+\underset{–}{27+8}]$

$=5+7x[12x+35]$

$\underset{–}{\text{Step 2:}}$
Now, expanding the square bracket:
$5+7x[12x+35]$

$=5+7x\times 12x+7x\times 35$

$=5+(7\times 12)\cdot x^{(1+1)}+(7\times 35)\cdot x$
$[\because a^m\times a^n=a^{m+n}]$

$=5+84x^2+245x$ $[\because 7\times 12=84,7\times 35=245]$

$=84x^2+245x+5$

As a result, the expression $5+7x\left[3\right(4x+9)+8]$ on simplification would give $84x^2+245x+5$.

Therefore, option (d.) is the correct answer.