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Question

Simplify

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

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Solution

(3x2 + 5x − 7)(x − 1)

By column method:

3x2 +5x -7 × (x -1) 3x3 +5x2 -7x -3x2 -5x +7 Add: 3x3 +2x2 -12x+7


(x2 − 2x + 3)(x + 4)

By column method:

x2 -2x +3 × (x +4) x3 -2x2 +3x 4x2 -8x +12 Add: x3 +2x2 -5x +12

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

=3x3 +2x2 -12x +7 -(x3+2x2 -5x +12)=3x3-x3 +2x2 -2x2 -12x +5x +7 -12=2x3 -7x -5

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