Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Algebraic Expressions and Identities - Exercise 6.7
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Page 1 Q u e s t i o n : 1 1 5 Find the following products: i (x + 4) (x + 7) ii (x - 11) (x + 4) iii (x + 7) (x - 5) iv (x - 3) ( x - 2) v (y 2 - 4) (y 2 - 3) vi x+43x+34 vii (3x + 5) (3x + 11) viii (2x 2 - 3) (2x 2 + 5) ix (z 2 + 2) (z 2 - 3) x (3x - 4y) (2x - 4y) xi (3x 2 - 4xy) (3x 2 - 3xy) xii x+15(x + 5) xiii z+34z+43 xiv (x 2 + 4) (x 2 + 9) xv (y 2 + 12) (y 2 + 6) xvi y2+57y2-145 xvii (p 2 + 16) p2-14 S o l u t i o n : i Here, we will use the identity x+ax+b=x2+a+bx+ab. x+4x+7=x2+4+7x+4×7=x2+11x+28 ii Here, we will use the identity x-ax+b=x2+b-ax-ab. x-11x+4=x2+4-11x-11×4=x2-7x-44 iii Here, we will use the identity ? x+ax-b=x2+a-bx-ab. x+7x-5=x2+7-5x-7×5=x2+2x-35 iv Here, we will use the identity ? x-ax-b=x2-a+bx+ab. x-3x-2=x2-3+2x+3×2=x2-5x+6 v Here, we will use the identity ? x-ax-b=x2-a+bx+ab. y2-4y2-3=y22-4+3y2+4×3=y4-7y2+12 vi Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x+43x+34=x2+43+34x+43×34=x2+2512x+1 vii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. 3x+53x+11=3x2+5+113x+5×11=9x2+48x+55 viii Here, we will use the identity ? x-ax+b=x2+b-ax-ab. 2x2-32x2+5=2x22+5-32x2-3×5=4x4+4x2-15 ix Here, we will use the identity ? x+ax-b=x2+a-bx-ab. z2+2z2-3=z22+2-3z2-2×3=z4-z2-6 x Here, we will use the identity ? x-ax-b=x2-a+bx+ab. 3x-4y2x-4y=4y-3x4y-2x (Taking common -1 from both parentheses)=4y2-3x+2x4y+3x×2x=16y2-12xy+8xy+6x2=16y2-20xy+6x2 xi Here, we will use the identity ? x-ax-b=x2-a+bx+ab. 3x2-4xy3x2-3xy=3x22-4xy+3xy3x2+4xy×3xy=9x4-12x3y+9x3y+12x2y2=9x4-21x3y+12x2y2 xii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x+15x+5=x2+15+5x+15×5=x2+265x+1 xiii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. z+34z+43=z2+34+43x+34×43=z2+2512z+1 xiv Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x2+4x2+9=x22+4+9x2+4×9=x4+13x2+36 xv Here, we will use the identity ? x+ax+b=x2+a+bx+ab. y2+12y2+6=y22+12+6y2+12×6=y4+18y2+72 xvi Here, we will use the identity ? x+ax-b=x2+a-bx-ab. y2+57y2-145=y22+57-145y2-57×145=y4-7335y2-2 xvii Here, we will use the identity ? x+ax-b=x2+a-bx-ab. p2+16p2-14=p22+16-14p2-16×14=p4+634p2-4 Q u e s t i o n : 1 1 6 Evaluate the following: i 102 × 106 ii 109 × 107 iii 35 × 37 iv 53 × 55 v 103 × 96 vi 34 × 36 vii 994 × 1006 S o l u t i o n : i Here, we will use the identity x+ax+b=x2+a+bx+ab 102×106=100+2100+6=1002+2+6100+2×6=10000+800+12=10812 ii Here, we will use the identity x+ax+b=x2+a+bx+ab 109 × 107=100+9100+7=1002+9+7100+9×7=10000+1600+63=11663 iii Here, we will use the identity x+ax+b=x2+a+bx+ab 35 × 37=30+530+7=302+5+730+5×7=900+360+35=1295 iv Here, we will use the identity x+ax+b=x2+a+bx+ab 53 × 55=50+350+5=502+3+550+3×5=2500+400+15=2915 Page 2 Q u e s t i o n : 1 1 5 Find the following products: i (x + 4) (x + 7) ii (x - 11) (x + 4) iii (x + 7) (x - 5) iv (x - 3) ( x - 2) v (y 2 - 4) (y 2 - 3) vi x+43x+34 vii (3x + 5) (3x + 11) viii (2x 2 - 3) (2x 2 + 5) ix (z 2 + 2) (z 2 - 3) x (3x - 4y) (2x - 4y) xi (3x 2 - 4xy) (3x 2 - 3xy) xii x+15(x + 5) xiii z+34z+43 xiv (x 2 + 4) (x 2 + 9) xv (y 2 + 12) (y 2 + 6) xvi y2+57y2-145 xvii (p 2 + 16) p2-14 S o l u t i o n : i Here, we will use the identity x+ax+b=x2+a+bx+ab. x+4x+7=x2+4+7x+4×7=x2+11x+28 ii Here, we will use the identity x-ax+b=x2+b-ax-ab. x-11x+4=x2+4-11x-11×4=x2-7x-44 iii Here, we will use the identity ? x+ax-b=x2+a-bx-ab. x+7x-5=x2+7-5x-7×5=x2+2x-35 iv Here, we will use the identity ? x-ax-b=x2-a+bx+ab. x-3x-2=x2-3+2x+3×2=x2-5x+6 v Here, we will use the identity ? x-ax-b=x2-a+bx+ab. y2-4y2-3=y22-4+3y2+4×3=y4-7y2+12 vi Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x+43x+34=x2+43+34x+43×34=x2+2512x+1 vii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. 3x+53x+11=3x2+5+113x+5×11=9x2+48x+55 viii Here, we will use the identity ? x-ax+b=x2+b-ax-ab. 2x2-32x2+5=2x22+5-32x2-3×5=4x4+4x2-15 ix Here, we will use the identity ? x+ax-b=x2+a-bx-ab. z2+2z2-3=z22+2-3z2-2×3=z4-z2-6 x Here, we will use the identity ? x-ax-b=x2-a+bx+ab. 3x-4y2x-4y=4y-3x4y-2x (Taking common -1 from both parentheses)=4y2-3x+2x4y+3x×2x=16y2-12xy+8xy+6x2=16y2-20xy+6x2 xi Here, we will use the identity ? x-ax-b=x2-a+bx+ab. 3x2-4xy3x2-3xy=3x22-4xy+3xy3x2+4xy×3xy=9x4-12x3y+9x3y+12x2y2=9x4-21x3y+12x2y2 xii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x+15x+5=x2+15+5x+15×5=x2+265x+1 xiii Here, we will use the identity ? x+ax+b=x2+a+bx+ab. z+34z+43=z2+34+43x+34×43=z2+2512z+1 xiv Here, we will use the identity ? x+ax+b=x2+a+bx+ab. x2+4x2+9=x22+4+9x2+4×9=x4+13x2+36 xv Here, we will use the identity ? x+ax+b=x2+a+bx+ab. y2+12y2+6=y22+12+6y2+12×6=y4+18y2+72 xvi Here, we will use the identity ? x+ax-b=x2+a-bx-ab. y2+57y2-145=y22+57-145y2-57×145=y4-7335y2-2 xvii Here, we will use the identity ? x+ax-b=x2+a-bx-ab. p2+16p2-14=p22+16-14p2-16×14=p4+634p2-4 Q u e s t i o n : 1 1 6 Evaluate the following: i 102 × 106 ii 109 × 107 iii 35 × 37 iv 53 × 55 v 103 × 96 vi 34 × 36 vii 994 × 1006 S o l u t i o n : i Here, we will use the identity x+ax+b=x2+a+bx+ab 102×106=100+2100+6=1002+2+6100+2×6=10000+800+12=10812 ii Here, we will use the identity x+ax+b=x2+a+bx+ab 109 × 107=100+9100+7=1002+9+7100+9×7=10000+1600+63=11663 iii Here, we will use the identity x+ax+b=x2+a+bx+ab 35 × 37=30+530+7=302+5+730+5×7=900+360+35=1295 iv Here, we will use the identity x+ax+b=x2+a+bx+ab 53 × 55=50+350+5=502+3+550+3×5=2500+400+15=2915 v Here, we will use the identity x+ax-b=x2+a-bx-ab 103 × 96=100+3100-4=1002+3-4100-3×4=10000-100-12=9888 vi Here, we will use the identity x+ax+b=x2+a+bx+ab 34 × 36=30+430+6=302+4+630+4×6=900+300+24=1224 vii Here, we will use the identity x-ax+b=x2+b-ax-ab 994 × 1006=1000-6×1000+6=10002+6-6×1000-6×6=1000000-36=999964 Processing math: 36% Contrib /a11y/accessibility-menu.jsRead More
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