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(1.5x - 4y) (1.5x + 4y + 3) - 4.5x + 12y = 1.5x(1.5x + 4y +3) - 4y(1.5x + 4y +3) - 4.5x +12y = (1.5x X 1.5x) + (1.5x X 4y) + (1.5x X 3) - (4y X 1.5x) - (4y X 4y) - (4y x 3) - 4.5x +12y = 2.25x 2 + 6xy + 4.5x - 6xy - 16y 2 - 12y - 4.5x + 12y = 2.25x 2 + ( 6 - 6)xy + (4.5 - 4.5)x - 16y 2 + (12 - 12)y = 2.25x 2 + 0 + 0 - 16y 2 + 0 = 2.25x 2 - 16y 2

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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

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

= 2.25x²+ 6xy + 4.5x - 6xy - 16y²- 12y - 4.5x + 12y
= 2.25x²+ ( 6 - 6)xy + (4.5 - 4.5)x - 16y²+ (12 - 12)y
= 2.25x²+ 0 + 0 - 16y² + 0
= 2.25x²- 16y²