Multiply :
(i) 8ab2 by −4a3b4(ii) 23ab by −14a2b(iii) −5cd2 by −5cd2(iv) 4a and (6a+7)(v) −8x and (4−2x−x2)(vi) 2a2−5a−4 and −3a.(vii) x+4 by x−5(viii) 5a−1 by 7a−3(ix) 12a+5b by 7a−b(x) x2+x+1 by 1−x(xi)2m2−3m−1 and 4m2−m−1(xii) a2,ab and b2(xiii) abx,−3a2x and 7b2x3(xiv) −3bx,−5xy and −7b3y2(xv) (−32x5y3) and (49a2x3y)(xvi) (−23a7b2) and (−94ab5)(xvii)(2a3−3a2b2) and (−12ab2)(xviii)(2x+12y) and (2x−12y)
Multiply :
(i) 8ab2 by −4a3b4(ii) 23ab by −14a2b(iii) −5cd2 by −5cd2(iv) 4a and (6a+7)(v) −8x and (4−2x−x2)(vi) 2a2−5a−4 and −3a.(vii) x+4 by x−5(viii) 5a−1 by 7a−3(ix) 12a+5b by 7a−b(x) x2+x+1 by 1−x(xi)2m2−3m−1 and 4m2−m−1(xii) a2,ab and b2(xiii) abx,−3a2x and 7b2x3(xiv) −3bx,−5xy and −7b3y2(xv) (−32x5y3) and (49a2x3y)(xvi) (−23a7b2) and (−94ab5)(xvii)(2a3−3a2b2) and (−12ab2)(xviii)(2x+12y) and (2x−12y)
(i) 8ab2 × −4a3b4=(8×−4)(ab2 ×a3b4)=−32a1+3.b2+4=−32a4b6 Ans.(ii) 23ab × −14a2b=(23×−14)(ab×a2b)=−16a1+2.b1+1=−16a3b2(iii) −5cd2 × −5cd2=(−5×−5)(cd2 ×cd2)=25c1+1d2+2=25c2d4 Ans.(iv) 4a(6a+7)=4a×6a+4a×7=24a2+28a Ans.(v) −8x (4−2x−x2)=−8x×4−8x×−2x−8x×−x2=−32x+16x2+8x3 Ans.(vi)−3a(2a2−5a−4)=−3a×2a2−5a×−3a−4×−3a=−6a3+15a2+12a Ans.(vii) (x+4) (x−5)=x(x−5)+4(x−5)=x2−5x+4x−20=x2−x−20 Ans.(viii) (5a−1) (7a−3)=5a(7a−3)−1(7a−3)=35a2−15a−7a+3=35a2−22a+3 Ans.(ix) (12a+5b)(7a−b)=12a(7a−b)+5b(7a−b)=84a2−12ab+35ab−5b2=84a2+23ab−5b2 Ans.(x) (x2+x+1) (1−x)=1(x2+x+1)−x(x2+x+1)=x2+x+1−x3−x2−x.=1−x3 Ans.(xi)2(m2−3m−1 ) (4m2−m−1)=2m2(4m2−m−1)−3m(4m2−m−1)−1(4m2−m−1)=8m4−2m3−2m2−12m3+3m2+3m−4m2+m+1=8m4−14m3−6m2+3m2+4m+1=8m4−14m3−3m2+4m+1 Ans.(xii) a2×ab × b2=a2+1.b1+2=a3b3 Ans.(xiii) abx×−3a2x × 7b2x3=(−3×7)(a×a2)(b×b2)(x×x×x3)=−21a3b3x5 Ans.(xiv) −3bx×−5xy × −7b3y2=(−3×−5×−7)(b×b3)(x×x)(y×y2)=−105b4x2y3(xv) (−32x5y3)(49a2x3y)=(−32×49)(a)2(x5×x3)(y3×y)=−23a2x8 y4 Ans.(xvi) (−23a7b2)(−94ab5)=(−23×−94)(a7×a)(b2×b5)=32a8b7 Ans.(xvii) (2a3−3a2b)(−12ab2)=−12ab2(2a3−3a2b)=2a3×−12ab2−3a2b×−12ab2=−a4b4+32a3b3 Ans.(xviii)(2x+12y)(2x−12y)=2x(2x−12y)+12(2x−12y)=4x2−xy+xy−14y2=4x2−14y2 Ans.
(i) 8ab2 × −4a3b4=(8×−4)(ab2 ×a3b4)=−32a1+3.b2+4=−32a4b6 Ans.(ii) 23ab × −14a2b=(23×−14)(ab×a2b)=−16a1+2.b1+1=−16a3b2(iii) −5cd2 × −5cd2=(−5×−5)(cd2 ×cd2)=25c1+1d2+2=25c2d4 Ans.(iv) 4a(6a+7)=4a×6a+4a×7=24a2+28a Ans.(v) −8x (4−2x−x2)=−8x×4−8x×−2x−8x×−x2=−32x+16x2+8x3 Ans.(vi)−3a(2a2−5a−4)=−3a×2a2−5a×−3a−4×−3a=−6a3+15a2+12a Ans.(vii) (x+4) (x−5)=x(x−5)+4(x−5)=x2−5x+4x−20=x2−x−20 Ans.(viii) (5a−1) (7a−3)=5a(7a−3)−1(7a−3)=35a2−15a−7a+3=35a2−22a+3 Ans.(ix) (12a+5b)(7a−b)=12a(7a−b)+5b(7a−b)=84a2−12ab+35ab−5b2=84a2+23ab−5b2 Ans.(x) (x2+x+1) (1−x)=1(x2+x+1)−x(x2+x+1)=x2+x+1−x3−x2−x.=1−x3 Ans.(xi)2(m2−3m−1 ) (4m2−m−1)=2m2(4m2−m−1)−3m(4m2−m−1)−1(4m2−m−1)=8m4−2m3−2m2−12m3+3m2+3m−4m2+m+1=8m4−14m3−6m2+3m2+4m+1=8m4−14m3−3m2+4m+1 Ans.(xii) a2×ab × b2=a2+1.b1+2=a3b3 Ans.(xiii) abx×−3a2x × 7b2x3=(−3×7)(a×a2)(b×b2)(x×x×x3)=−21a3b3x5 Ans.(xiv) −3bx×−5xy × −7b3y2=(−3×−5×−7)(b×b3)(x×x)(y×y2)=−105b4x2y3(xv) (−32x5y3)(49a2x3y)=(−32×49)(a)2(x5×x3)(y3×y)=−23a2x8 y4 Ans.(xvi) (−23a7b2)(−94ab5)=(−23×−94)(a7×a)(b2×b5)=32a8b7 Ans.(xvii) (2a3−3a2b)(−12ab2)=−12ab2(2a3−3a2b)=2a3×−12ab2−3a2b×−12ab2=−a4b4+32a3b3 Ans.(xviii)(2x+12y)(2x−12y)=2x(2x−12y)+12(2x−12y)=4x2−xy+xy−14y2=4x2−14y2 Ans.
