Question

Subtract the sum of $12ab-10b^2-18a^2$ and $9ab+12b^2+14a^2$ from the sum of $ab+2b^2$ and $3b^2-a^2.$

• A. $3a^2+3b^2+20ab$
• B. $3a^2+3b^2-20ab$
• C. $a^2+b^2-20ab$
• D. $3a^2+3b^2-20ab$

Answer 1

The correct option is D $3a^2+3b^2-20ab$

Sum of $12ab-10b^2-18a^{2}and9ab+12b^2+14a^2$
$=12ab-10b^2-18a^2+9ab+12b^2+14a^2$
On combining the like terms,
$=(12ab+9ab)+(-10b^2+12b^2)+(-18a^2+14a^2)$
Solving the groups,
$=ab(12+9)+b^2(-10+12)+a^2(-18+14)$
$=21ab+2b^2-4a^2$

Sum of $ab+2b^2$ and $3b^2-a^2$
$=ab+2b^2+3b^2-a^2$
On combining the like terms,
$=ab+(2b^2+3b^2)-a^2$
$=ab+5b^2-a^2$

Now, subtracting $21ab+2b^2-4a^2$ from $ab+5b^2-a^2$, we get
$=(ab+5b^2-a^2)-(21ab+2b^2-4a^2)=ab+5b^2-a^2-21ab-2b^2+4a^2$
On combining the like terms,
$=(ab-21ab)+(5b^2-2b^2)+(-a^2+4a^2)$
Solving the groups,
$=-20ab+3b^2+3a^2=3a^2+3b^2-20ab$