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,7a2b2
iv) a2-9,4a
v) pq+qr+rp,0
i) 4p,q+r
Sol.:
=4p(q+r)
=4p×q+4p×r
=4pq+4qr
Answer:
=4pq+4qr
ii) ab,a-b
=ab(a-b)
=ab×a-ab×b
=a2b-ab2
Answer:
=a2b-ab2
iii) a+b,7a2b2
=7a2b2(a+b)
=7a2b2×a+7a2b2×b
=7a3b2+7a2b3
Answer:
=7a3b2+7a2b3
iv) a2-9,4a
=4a(a2-9)
=4a2×a-4a×9
=4a3-36
Answer:
=4a3-36
v) pq+qr+rp,0
=0(pq+qr+rp)
=0
Answer:
=0
Q2. Complete the table.
=a(b+c+d)
=a×b+a×c+a×d
=ab+ac+ad
Answer:
=ab+ac+ad
ii)
=5xy(x+y-5)
=5xy×x+5xy×y-5xy×5
=5x2y+5xy2-25xy
Answer:
=5x2y+5xy2-25xy
iii)
=p(6p2-7p+5)
=p×6p2-p×7p+p×5
=6p3-7p2+5p
Answer:
=6p3-7p2+5p
iv)
=4p2q2(p2-q2)
=4p2q2×p2-4p2q2×q2
=4p4q2-4p2q4
Answer:
=4p4q2-4p2q4
v)
=abc(a+b+c)
=abc×a+abc×b+abc×c
=a2bc+ab2c+abc2
Answer:
=a2bc+ab2c+abc2
Q3. Find the product.
i) (a2)×(2a22)×(4a26)
ii) (23xy)×(-910x2y2)
iii) (-103pq3)×(65p3q)
iv) x×x2×x3×x4
i) (a2)×(2a22)×(4a26)
=1×2×4a2+22+26
=8a50
Answer:
=8a50
ii) (23xy)×(-910x2y2)
=23×(-910)×x1+2×y1+2
=-1830x3y3
Answer:
=-1830x3y3
iii) (-103pq3)×(65p3q)
=-103×65×p3+3×q3+3
=-6015p6q6
Answer:
=-6015p6q6
iv) x×x2×x3×x4
=x1+2+3+4
=x10
Answer:
=x10
Q4.
a) Simplify 3x(4x-5)+3 and find its values for i) x=3 ii) x=12
b) Simplify a(a2+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=12
=3x×4x-3x×5+3
=12x2-15x+3
i) For x=3
=12×(3)2-15x+3
=12×9-15×3+3
=108-45+3
=111-45
=66
Answer:
=66
ii) For x=12
=12×(12)2-15×12+3
=12×14-152+3
=3-152+3
=6-152
=12-152
=-32
Answer:
=-32
b) Simplify a(a2+a+1)+5 and find its values for i) a=0, ii) a=1, iii) a=-1
=a(a2+a+1)+5
=a×a2+a×a+1×a+5
=a1+2+a1+1+a+5
=a3+a2+a+5
i) For a=0
=03+02+0+5
=0+5
=5
Answer:
=5
ii) For a=1
=13+12+1+5
=1+1+1+5
=8
Answer:
=8
iii) For a=-1
=(-1)3+(-1)2+(-1)+5
=-1+1-1+5
=4
Answer:
=4
Q5.
a) Add: p(p-q),q(q-r)
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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