KSEEB Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3
KSEEB Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3
KSEEB Solutions for Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3
Question 1.
Carry out the multiplication of the expression 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
Solution:
(i) 4p(q + r)
= 4p × q + 4p × r
= 4pq + 4pr
(ii) ab × (a – b)
= ab × a – ab × b
= a2b – ab2
(iii) (a + b) (7a2b2)
= a × 7a2b2 + b × 7a2b2
= 7a3b2 + 7a2b3
(iv) (a2 – 9) (4a)
= a2 × 4a – 9 × 4a
= 4a3 – 36a
(v) (pq +qr + rp) (0) = 0
Question 2.
Complete the table.
Solution:
(i) (a) (b + c + d)
= (ab + ac + ad)
(ii) (x + y – 5)(5xy)
= 5xy(x + y – 5)
= 5yx × x + 5xy × y – 5 × 5xy
= 5x2y + 5xy2 × -25xy
(iii) p(6p2 – 7p + 5)
= p × 6p2 – 7p × p + p × 5)
= 6p3 – 7p2 + 5p
(iv) 4p2q2(p2 – q2)
= 4p2q2 × p2 – 4p2q2 × q2
= 4p4q2 – 4p2q4
(v) (a + b + c) (abc)
= a × abc + b × abc + c × abc
= a2bc + ab2c + abc2
Question 5.
(a) Add: p(p – q), q(q – r) and r(r – p)
(b) Add: 2x(z – x – y) and 2y(z – y – x)
(c) Subtract: 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)
(d) Subtract: 3a(a + b + c) – 2b(a – b + c) from 4c(-a + b + c)
Solution:
(a) p(p – q), q(q – r) and r(r – p)
= p × p – p × q + q × q – q × r + r × r – r × p
= p × p – pq + q × q – qr + r × r – rp
= p2 – pq + q2 – qr + r2 – rp
= p2 + q2 + r2 – pq – qr – rp
(b) 2x(z – x – y) and 2y(z – y – x)
= 2xz – 2x × x – 2x × y and 2y × z – 2y × y – 2y × x)
= 2xz – 2x2 – 2xy and 2yz – 2y2 – 2yx
= 2xz – 2x2 – 2xy – 2yx – 2y2 + 2yz
= 2xz – 2x2 – 4xy – 2y2 + 2yz
(c) 3l(l – 4m + 5n) from 4l(10n – 3m + 2l)
= 3l × l – 3l × 4m + 3l × 5n from 4l × 10n – 4l × 3m + 4l × 2l
= 3l2 – 12lm + 15ln from 40ln – 12lm + 8l2
= 40ln – 12lm + 8l2 – 15ln + 12lm + 3l2
= 25ln + 0 + 5l2
(d) 3a(a + b + c) – 2b(a – b + c) from 4c(-a + b + c)
= 3a × a + 3a × b + 3a × c – 2b × a + 2b × b × b – 2b × c
from -4ca + 4cb + 4c × c = 3a2 + 3ab + 3ac
-2ab + 2b2 × 2bc
from -4ca + 4bc + 4c2 = -4ca + 4bc + 4c2
= -3ac + 2bc + 3a2 + 2b2 + 3ab
= -7ac – 6bc + 4a2 – 3a2 – 2b2 + 3ab
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