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Question

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

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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$=\left(2{a}^{2}+ab-{b}^{2}\right)+\left(-{a}^{2}+2ab+3{b}^{2}\right)+\left(3{a}^{2}-10ab+4{b}^{2}\right)$grouping the like terms$=\left(2{a}^{2}-{a}^{2}+3{a}^{2}\right)+\left(ab+2ab-10ab\right)+\left(-{b}^{2}+3{b}^{2}+4{b}^{2}\right)$adding the numerical coefficients$=\left(2-1+3\right){a}^{2}+\left(1+2-10\right)ab+\left(-1+3+4\right){b}^{2}\phantom{\rule{0ex}{0ex}}=\left(5-1\right){a}^{2}+\left(3-10\right)ab+\left(-1+7\right){b}^{2}\phantom{\rule{0ex}{0ex}}=4{a}^{2}+\left(-7\right)ab+6{b}^{2}\phantom{\rule{0ex}{0ex}}=4{a}^{2}-7ab+6{b}^{2}$

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