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Question

# Simplify each of the following: (i) x2−3x+5−12(3x2−5x+7)(ii) [5−3x+2y−(2x−y)]−(3x−7y+9)(iii) 112x2y−94xy2+14xy−114y2x+115yx2+12xy(iv) (13y2−47y+11)−(17y−3+2y2)−(27y−23y2+2)(v) −12a2b2c+13ab2c−14abc2−15cb2a2+16cb2a−17c2ab+18ca2b.

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Solution

## (i) x2−3x+5−12(3x2−5x+7)=x2−3x+5−32x2+52x−72=x2−32x2−3x+52x+5−72=(1−32)x2−(3−52)x+(51−72)=2−32x2−6−52x+10−72=−12x2−12x+32(ii) [5−3x+2y−(2x−y)]−(3x−7y+9)=[5−3x+2y−2x+y]−(3x−7y+9)=5−3x+2y−2x+y−3x+7y−9=5−9−3x−2x−3x+2y+y+7y=−4−8x+10y(iii) 112x2y−94xy2+14xy−114y2x+115yx2+12xy=112x2y+115yx2−94xy2−114y2x+14xy+12xy=(112+115)x2y−(94+114)xy2+(14+12)xy=165+230x2y−63+228xy2+1+24xy=16730x2y−6528xy2+34xy(iv) (13y2−47y+11)−(17y−3+2y2)−(27y−23y2+2)=13y2−47y+11−17y+3−2y2−27y+23y2−2=13y2−2y2+23y2−47y−17y−27y+11+3−2=(13−21+23)y2−(47+17+27)y+12=1−6+23y2−4+1+27y+12=−33y2−77y+12=−1y2=1y+12=−y2−y+12(v) −12a2b2c+13ab2c−14abc2−15cb2a2+16cb2a−17c2ab+18ca2b=−12a2b2c−15a2b2c+13ab2c+16ab2c−14abc2−17abc2+18ca2b=(−12−15)a2b2c+(13+16)ab2c−(14+17)abc2+18a2bc=−5−210a2b2c+2+16ab2c−7+428abc2+18a2bc=−710a2b2c+36ab2c−1128abc2+18a2bc=−710a2b2c+12ab2c−1128abc2+18a2bc

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