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(a +b + c)(a + b + c) =a (a + b - c) + b( a 9 b - c) + c(a + b - c) = ( a x a) + ( a x b) - ( a x c) + ( b x a) + ( b x b) - ( b x c) + ( c x a) + ( c x b) - (c x c) = a 2 + ab - ac + ab + b 2 - bc + ac + bc - c 2 = a 2 +2ab + b 2 - c 2 = a 2 + b 2 - c 2 + 2ab

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Algebraic Expressions and Identities

Short Answer Type

81.

Simplify:

(x + y) (x²-xy + y²)

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82.

Simplify:

(1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y

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83.
Simplify:

(a +b + c)(a + b + c)

(a +b + c)(a + b + c)

                   =a (a + b - c) + b( a 9 b - c) + c(a + b - c)

                   = ( a x a) + ( a x b) - ( a x c) + ( b x a) + ( b x b) - ( b x c)
                      + ( c x a) + ( c x b) - (c x c)

                   = a²+ ab - ac + ab +b² - bc + ac + bc - c²
                   = a²+2ab +b² - c²                   = a²+b² - c²+ 2ab