Find the sum of the expressions
$2 a^{2} + a b - b^{2}; - a^{2} + 2 a b + 3 b^{2}; 3 a^{2} - 10 a b + 4 b^{2}$

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Solution

To add two or more algebraic expressions, group the like terms of the expression and add each group of like terms separately.
The Sum
$= (2 a^{2} + a b - b^{2}) + (- a^{2} + 2 a b + 3 b^{2}) + (3 a^{2} - 10 a b + 4 b^{2})$
grouping the like terms
$= (2 a^{2} - a^{2} + 3 a^{2}) + (a b + 2 a b - 10 a b) + (- b^{2} + 3 b^{2} + 4 b^{2})$
adding the numerical coefficients
$= (2 - 1 + 3) a^{2} + (1 + 2 - 10) a b + (- 1 + 3 + 4) b^{2} = (5 - 1) a^{2} + (3 - 10) a b + (- 1 + 7) b^{2} = 4 a^{2} + (- 7) a b + 6 b^{2} = 4 a^{2} - 7 a b + 6 b^{2}$

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Question 58 (f)

Subtract:

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

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} .

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(5 a - 4 b)^{2}

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