Question 71

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

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Solution

Sum of $12 a b - 10 b^{2} - 18 a^{2} a n d 9 a b + 12 b^{2} + 14 a^{2}$
$= 12 a b - 10 b^{2} - 18 a^{2} + 9 a b + 12 b^{2} + 14 a^{2}$
On combining the like terms,
$= 12 a b + 9 a b - 10 b^{2} + 12 b^{2} - 18 a^{2} + 14 a^{2} = 21 a b + 2 b^{2} - 4 a^{2}$
Sum of $a b + 2 b^{2}$ and $3 b^{2} - a^{2}$
$= a b + 2 b^{2} + 3 b^{2} - a^{2} = a b + 5 b^{2} - a^{2}$
Now, subtracting $21 a b + 2 b^{2} - 4 a^{2}$ from $a b + 5 b^{2} - a^{2}$ , we get
$= (a b + 5 b^{2} - a^{2}) - (21 a b + 2 b^{2} - 4 a^{2}) = a b + 5 b^{2} - a^{2} - 21 a b - 2 b^{2} + 4 a^{2}$
On combining the like terms,
$= a b - 21 a b + 5 b^{2} - 2 b^{2} - a^{2} + 4 a^{2} = - 20 a b + 3 b^{2} + 3 a^{2} = 3 a^{2} + 3 b^{2} - 20 a b$

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Similar questions

12 a b - 10 b^{2} - 18 a^{2}

9 a b + 12 b^{2} + 14 a^{2}

a b + 2 b^{2}

3 b^{2} - a^{2} .

12 a b - 10 b^{2} - 18 a^{2}

9 a b + 12 b^{2} + 14 a^{2}

a b + 2 b^{2}

3 b^{2} - a^{2} .

Question 58 (f)

Subtract:

$- 2 a^{2} - 2 b^{2}$ from $- a^{2} - b^{2} + 2 a b .$

{9 b}^{2} + {3 c}^{2}

{2 b}^{2} + b c + {2 c}^{2}

{2 b}^{2} - 2 b c - c^{2}

c^{2} + 2 b c - b^{2}

How much should $3 x y - 4 a^{2} + 5 b^{2} + 2$ be increased to get $- 5 + 4 a^{2} + 2 b^{2} - 7 x y$ ?

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