8th Maths 9.4

Chapter 9 Algebraic Expressions and Identities

NCERT Class 8th solution of Exercise 9.1

NCERT Class 8th solution of Exercise 9.2

NCERT Class 8th solution of Exercise 9.3

NCERT Class 8th solution of Exercise 9.5

Exercise 9.4

Q1. Multiply the binomials.

$(2x + 5) text{ and } (4x - 3)$

ii)

$(y - 8) text{ and } (3y - 4)$

iii)

$(2.5l - 0.5m) text{ and } (2.5l + 0.5m)$

iv)

$(a + 3b) text{ and }(x + 5}$

$(2pq + 3q^2) text{ and }(3pq - 2q^2)$

vi)

$(3/4a^2 + 3b^2) text{ and }4(a^2 - 2/3b^2)$

$(2x + 5) text{ and } (4x - 3)$

$text{Sol.}$

$=(2x+5)times(4x-3)$

$=2x(4x-3)+5(4x-3)$

$=2x times 4x - 2x times 3+5times4x-5times3$

$=8x^2-6x+20x-15$

$=8x^2+14x-15$

$text{Answer:}$

$=8x^2+14x-15$

ii)

$(y - 8) text{ and } (3y - 4)$

$text{Sol.}$

$=(y - 8)times(3y - 4)$

$=y(3y-4)-8(3y-4)$

$=ytimes3y-ytimes4-8times3y+8times4$

$=3y^2-4y-24y+32$

$=3y^2-28y+32$

$text{Answer:}$

$=3y^2-28y+32$

iii)

$(2.5l - 0.5m) text{ and } (2.5l + 0.5m)$

$text{Sol.}$

$=(2.5l - 0.5m)times(2.5l + 0.5m)$

$=2.51(2.51+0.5m)-0.5m(2.51+0.5m)$

$=2.5l times 2.5l + 2.5l times 0.5m - 0.5m times 2.5l$

$-0.5m times 0.5m$

$=6.25l^2+1.25ml-1.25ml-0.25m^2$

$=6.25l^2-0.25m^2$

$text{Answer:}$

$=6.25l^2-0.25m^2$

iv)

$(a + 3b) text{ and }(x + 5}$

$text{Sol.}$

$=(a + 3b)times(x + 5)$

$=a(x+5)+3b(x+5)$

$=a times x + a times 5+3b times x + 3btimes5$

$=ax+5a+3bx+15b$

$text{Answer:}$

$=ax+5a+3bx+15b$

$(2pq + 3q^2) text{ and }(3pq - 2q^2)$

$text{Sol.}$

$=(2pq + 3q^2)times(3pq - 2q^2)$

$=2pq(3pq-2q^2)+3q^2(3pq-2q^2)$

$=2pq times 3pq - 2pq times 2q^2 + 3q^2 times 3pq$

$-3q^2 times 2q^2$

$=6p^2q^2-4pq^3+9pq^3-6q^4$

$=6p^2q^2+5pq^3-6q^4$

$text{Answer:}$

$=6p^2q^2+5pq^3-6q^4$

vi)

$(3/4a^2 + 3b^2) text{ and }4(a^2 - 2/3b^2)$

$text{Sol.}$

$=(3/4a^2 + 3b^2)times4(a^2 - 2/3b^2)$

$=3/4a^2 times 4(a^2-2/3b^2)+3b^2times4(a^2-2/3b^2)$

$=3a^2times a^2 - 3a^2 times 2/3b^2 + 12b^2 times a^2$

$-12b^2times2/3b^2$

$=3a^4-2a^2b^2+12a^2b^2-8b^4$

$text{Answer:}$

$=3a^4-2a^2b^2+12a^2b^2-8b^4$

Q2. Find the product.

$(5 - 2x)(3 + x)$

ii)

$(x + 7y)(7x - y)$

iii)

$(a^2 + b)(a + b^2)$

iv)

$(p^2 - q^2)(2p + q)$

$(5 - 2x)(3 + x)$

$text{Sol.}$

$=(5 - 2x)times(3 + x)$

$=5(3 + x)-2x(3 + x)$

$=5times3 +5timesx-2x times 3 -2x timesx$

$=15+5x-6x-2x^2$

$=15-x-2x^2$

$text{Answer:}$

$=15-x-2x^2$

ii)

$(x + 7y)(7x - y)$

$text{Sol.}$

$=(x + 7y)times(7x - y)$

$=x(7x - y)+7y(7x - y)$

$=x times 7x - x times y + 7y times 7x - 7y times y$

$=7x^2-xy+49xy-7y^2$

$=7x^2+48xy-7y^2$

$text{Answer:}$

$=7x^2+48xy-7y^2$

iii)

$(a^2 + b)(a + b^2)$

$text{Sol.}$

$=(a^2 + b)(a + b^2)$

$=a^2(a + b^2)+b(a + b^2)$

$=a^2timesa +a^2 timesb^2 +b times a + b timesb^2$

$=a^3+a^2b^2+ab+b^3$

$text{Answer:}$

$=a^3+a^2b^2+ab+b^3$

iv)

$(p^2 - q^2)(2p + q)$

$text{Sol.}$

$=(p^2 - q^2)(2p + q)$

$=p^2(2p + q)-q^2(2p + q)$

$=p^2times2p+p^2q-q^2times2p-q^2 timesq$

$=2p^3+p^2q-2pq^2-q^3$

$text{Answer:}$

$=2p^3+p^2q-2pq^2-q^3$

Q3. Simplify.

$(x^2 - 5)(x + 5) + 25$

ii)

$(a^2 + 5)(b^3 + 3) + 5$

iii)

$(t + s^2)(t^2 - s)$

iv)

$(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$

$(x + y)(2x + y) + (x + 2y)(x - y)$

vi)

$(x + y)(x^2 - xy + y^2)$

vii)

$(1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y$

viii)

$(a + b + c)(a + b - c)$

$(x^2 - 5)(x + 5) + 25$

$text{Sol.}$

$=(x^2 - 5)(x + 5) + 25$

$=x^2(x+5)-5(x+5)+25$

$=x^3+5x^2-5x-25+25$

$=x^3+5x^2-5x$

$text{Answer:}$

$=x^3+5x^2-5x$

ii)

$(a^2 + 5)(b^3 + 3) + 5$

$text{Sol.}$

$=(a^2 + 5)(b^3 + 3) + 5$

$=a^2(b^3+3)+5(b^3+3)+5$

$=a^2b^3+3a^2+5b^3+15+5$

$=a^2b^3+3a^2+5b^3+20$

$text{Answer:}$

$=a^2b^3+3a^2+5b^3+20$

iii)

$(t + s^2)(t^2 - s)$

$text{Sol.}$

$=(t + s^2)(t^2 - s)$

$=t(t^2 - s)+s^2(t^2-s)$

$=t^3-st+s^2t^2-s^3$

$text{Answer:}$

$=t^3-st+s^2t^2-s^3$

iv)

$(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$

$text{Sol.}$

$=(a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)$

$=a(c - d)+b(c-d) + a(c + d)-b(c+d)$

$+ 2(ac + bd)$

$=ac-ad+bc-bd+ac+ad-bc-bd$

$+2ac+2bd$

$=2ac-2bd+2ac+2bd$

$=4ac$

$text{Answer:}$

$=4ac$

$(x + y)(2x + y) + (x + 2y)(x - y)$

$text{Sol.}$

$=(x + y)(2x + y) + (x + 2y)(x - y)$

$=x(2x+y)+y(2x+y)+x(x-y)$

$+2y(x-y)$

$=2x^2+xy+2xy+y^2+x^2-xy+2xy-2y^2$

$=3x^2+4xy-y^2$

$text{Answer:}$

$=3x^2+4xy-y^2$

vi)

$(x + y)(x^2 - xy + y^2)$

$text{Sol.}$

$=(x + y)(x^2 - xy + y^2)$

$=x(x^2-xy+y^2)+y(x^2-xy+y^2)$

$=x^3-x^2y+xy^2+x^2y-xy^2+y^3$

$=x^3+y^3$

$text{Answer:}$

$=x^3+y^3$

vii)

$(1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12y$

$text{Sol.}$

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

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

$=2.25x^2+6.0xy+4.5x-6.0xy-16y^2-12y-4.5x+12y$

$=2.25x^2-16y^2$

$text{Answer:}$

$=2.25x^2-16y^2$

viii)

$(a + b + c)(a + b - c)$

$text{Sol.}$

$=(a + b + c)(a + b - c)$

$=a(a+b-c)+b(a+b-c)+c(a+b-c)$

$=a^2+ab-ac+ab+b^2-bc+ac+bc-c^2$

$=a^2+2ab+b^2-c^2$

$=a^2+b^2-c^2+2ab$

$text{Answer:}$

$=a^2+b^2-c^2+2ab$

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8th Maths 9.4

Chapter 9

Algebraic Expressions and Identities

NCERT Class 8th solution of Exercise 9.1

NCERT Class 8th solution of Exercise 9.2

NCERT Class 8th solution of Exercise 9.3

NCERT Class 8th solution of Exercise 9.5

Exercise 9.4

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