Add the following
$- 6 a^{2} - 9 b^{2}, 7 a^{2} + 2 b^{2}, - 3 a^{2} - 4 b^{2}$

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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
$= (- 6 a^{2} - 9 b^{2}) + (7 a^{2} + 2 b^{2}) + (- 3 a^{2} - 4 b^{2}) = (- 6 a^{2} + 7 a^{2} - 3 a^{2}) + (- 9 b^{2} + 2 b^{2} - 4 b^{2})$ (grouping the like terms)
adding the numerical coefficient of like terms
$= (- 6 + 7 - 3) a^{2} + (- 9 + 2 - 4) b^{2} = (7 - 9) a^{2} + (- 13 + 2) b^{2} = - 2 a^{2} + (- 11) b^{2} = - 2 a^{2} - 11 b^{2}$

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