8th Maths 9.3
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 9.4
NCERT Class 8th solution of Exercise 9.5
Exercise 9.3
Q1. Carry out the multiplication of the expressions in each of the following pairs.
i) `4p, q+r`
ii) `ab, a - b`
iii) `a + b, 7a^2b^2`
iv) `a^2 - 9, 4a`
v) `pq + qr + rp, 0`
i) `4p, q+r`
`text{Sol.:}`
`=4p(q+r)`
`=4ptimesq+4ptimesr`
`=4pq+4qr`
`text{Answer:}`
`=4pq+4qr`
ii) `ab, a - b`
`=ab(a-b)`
`=abtimesa-abtimesb`
`=a^2b-ab^2`
`text{Answer:}`
`=a^2b-ab^2`
iii) `a + b, 7a^2b^2`
`=7a^2b^2(a+b)`
`=7a^2b^2timesa+7a^2b^2timesb`
`=7a^3b^2+7a^2b^3`
`text{Answer:}`
`=7a^3b^2+7a^2b^3`
iv) `a^2 - 9, 4a`
`=4a(a^2-9)`
`=4a^2timesa-4atimes9`
`=4a^3-36`
`text{Answer:}`
`=4a^3-36`
v) `pq + qr + rp, 0`
`=0(pq+qr+rp)`
`=0`
`text{Answer:}`
`=0`
Q2. Complete the table.
`=a(b+c+d)`
`=a timesb+a timesc+a times d`
`=ab+ac+ad`
`text{Answer:}`
`=ab+ac+ad`
ii)
`=5xy(x+y-5)`
`=5xy times x+5xy timesy -5xy times 5`
`=5x^2y+5xy^2-25xy`
`text{Answer:}`
`=5x^2y+5xy^2-25xy`
iii)
`=p(6p^2-7p+5)`
`=p times6p^2 - p times 7p + p times 5`
`=6p^3 - 7p^2 + 5p`
`text{Answer:}`
`=6p^3 - 7p^2 + 5p`
iv)
`=4p^2q^2(p^2-q^2)`
`=4p^2q^2 times p^2 - 4p^2q^2 timesq^2`
`=4p^4q^2-4p^2q^4`
`text{Answer:}`
`=4p^4q^2-4p^2q^4`
v)
`=abc(a+b+c)`
`=abc times a+abc times b+abc times c`
`=a^2bc+ab^2c+abc^2`
`text{Answer:}`
`=a^2bc+ab^2c+abc^2`
Q3. Find the product.
i) `(a^2)times(2a^22)times(4a^26)`
ii) `(2/3xy)times(-9/10x^2y^2)`
iii) `(-10/3pq^3)times(6/5p^3q)`
iv) `xtimesx^2timesx^3timesx^4`
i) `(a^2)times(2a^22)times(4a^26)`
`=1times2times4a^(2+22+26)`
`=8a^50`
`text{Answer:}`
`=8a^50`
ii) `(2/3xy)times(-9/10x^2y^2)`
`=2/3times(-9/10)timesx^(1+2)timesy^(1+2)`
`=-18/30x^3y^3`
`text{Answer:}`
`=-18/30x^3y^3`
iii) `(-10/3pq^3)times(6/5p^3q)`
`=-10/3times6/5timesp^(3+3)timesq^(3+3)`
`=-60/15p^6q^6`
`text{Answer:}`
`=-60/15p^6q^6`
iv) `xtimesx^2timesx^3timesx^4`
`=x^(1+2+3+4)`
`=x^10`
`text{Answer:}`
`=x^10`
Q4.
a) Simplify `3x(4x - 5) + 3` and find its values for i) `x = 3` ii) `x = 1/2`
b) Simplify `a(a^2 + a + 1) + 5` and find its values for i) `a = 0,` ii) `a = 1`, iii) `a = - 1`
a) Simplify `3x(4x - 5) + 3` and find its values for i) `x = 3` ii) `x = 1/2`
`=3xtimes4x-3xtimes5+3`
`=12x^2-15x+3`
i) `text{For }x=3`
`=12times(3)^2-15x+3`
`=12times9-15times3+3`
`=108-45+3`
`=111-45`
`=66`
`text{Answer:}`
`=66`
ii) `text{For }x=1/2`
`=12times(1/2)^2-15times1/2+3`
`=12times1/4-15/2+3`
`=3-15/2+3`
`=6-15/2`
`=(12-15)/2`
`=-3/2`
`text{Answer:}`
`=-3/2`
b) Simplify `a(a^2 + a + 1) + 5` and find its values for i) `a = 0,` ii) `a = 1`, iii) `a = - 1`
`=a(a^2+a+1)+5`
`=atimesa^2+atimesa+1timesa+5`
`=a^(1+2)+a^(1+1)+a+5`
`=a^3+a^2+a+5`
i) `text{For }a=0`
`=0^3+0^2+0+5`
`=0+5`
`=5`
`text{Answer:}`
`=5`
ii) `text{For }a=1`
`=1^3+1^2+1+5`
`=1+1+1+5`
`=8`
`text{Answer:}`
`=8`
iii) `text{For }a=-1`
`=(-1)^3+(-1)^2+(-1)+5`
`=-1+1-1+5`
`=4`
`text{Answer:}`
`=4`
Q5.
a) Add: `p(p - q), q(q - r) text{ and } r(r - p)`
b) Add: `2x(z - x - y) text{ and } 2y(z - y - x)`
c) Subtract: `3l(l - 4m + 5n) text{ from } 4l(10n - 3m + 2l)`
d) Subtract: `3a(a+ b + c) - 2b(a - b + c) text{ from }` `4c(-a + b + c)`
a) Add: `p(p - q), q(q - r) text{ and } r(r - p)`
`=p(p - q)+q(q - r)+r(r - p)`
`=p timesp-p timesq+q timesq-q timesr+r timesr``-r timesp`
`=p^2-pq+q^2-qr+r^2-rp`
`=p^2+q^2+r^2-pq+qr-rp`
`text{Answer:}`
`=p^2+q^2+r^2-pq+qr-rp`
b) Add: `2x(z - x - y) text{ and } 2y(z - y - x)`
`=2x(z - x - y)+2y(z - y - x)`
`=2xtimesz-2xtimesx-2xtimesy``+2ytimesz-2ytimesy-2ytimesx`
`=2xz-2x^2-2xy+2yz-2y^2-2xy`
`=-2x^2-2y^2+2xz-2xy-2xy+2yz`
`=-2x^2-2y^2-4xy+2yz+2zx`
`text{Answer:}`
`=-2x^2-2y^2-4xy+2yz+2zx`
c) Subtract: `3l(l - 4m + 5n) text{ from } 4l(10n - 3m + 2l)`
`=4l(10n-3m+21)-[3l(l-4m+5n)]`
`=4l times10n-4l times3m+4l times2l-3l timesl-3l`` times4m+3l times5n`
`=40ln-12lm+8l^2-3l^2-12lm+15ln`
`=5l^2+25ln`
`text{Answer:}`
`=5l^2+25ln`
d) Subtract: `3a(a+ b + c) - ``2b(a - b + c) text{ from }` `4c(-a + b + c)`
`=4c(-a + b + c)-[3a(a+b+c)-``2b(a-b+c)]`
`=-4ctimesa+4ctimesb+4ctimesc-[3atimesa``+3atimesb+3atimesc-2btimesa+2btimesb-2btimesc]`
`=-4ac+4bc+4c^2-3a^2-3ab-3ac+2ab``-2b^2+2bc`
`=-3a^2-2b^2+4c^2-ab+6bc-7ac`
`text{Answer:}`
`=-3a^2-2b^2+4c^2-ab+6bc-7ac`
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