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Addition and Subtraction of Algebraic Expression

If A=5p2-3q...

Question

If $A = 5 p^{2} - 3 q^{2} + r^{2}, B = - 2 q^{2} + 3 p^{2} - 4 r^{2}$ and $C = - 7 r^{2} + 3 p^{2} + 2 q^{2}$ .Find $A + B - C$

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Solution

$A + B = 5 p^{2} - 3 q^{2} + r^{2} + (- 2 q^{2} + 3 p^{2} - 4 r^{2})$

$= 5 p^{2} - 3 q^{2} + r^{2} - 2 q^{2} + 3 p^{2} - 4 r^{2}$

$= 8 p^{2} - 5 q^{2} - 3 r^{2}$

$A + B - C = 8 p^{2} - 5 q^{2} - 3 r^{2} - (- 7 r^{2} + 3 p^{2} + 2 q^{2})$

$= 8 p^{2} - 5 q^{2} - 3 r^{2} + 7 r^{2} - 3 p^{2} - 2 q^{2}$

$= 5 p^{2} - 7 q^{2} + 4 r^{2}$

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