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NCERT Solutions Class 8 Mathematics Solutions for Exercise 9.4 in Chapter 9 - Algebraic Expressions and Identities
Q1) Multiply the binomials:
(i) \left(2x+5\right)and\left(4x-3\right)
(ii) \left(y-8\right)\ and\ \left(3y-4\right)
(iii) \left(2.5l-0.5m\right)\ and\ \left(2.5l+0.5m\right)
(iv) \left(a+3b\right)\ and\ \ \left(x+5\right)
(v) \left(2pq+3q^2\right)\ and\ \left(3pq-2q^2\right)
(vi) \left(\frac{3}{4}a^2+3b^2\right)\ and\ 4\left(a^2-\frac{2}{3}b^2\right)
Solution:
(i) \left(2x+5\right)\times\left(4x-3\right)
= 2x\left(4x-3\right)+5\left(4x-3\right)
= 2x\times4x-2x\times3+5\times4x-5\times3
= 8x^2-6x+20x-15
= 8x^2+14x-15
(ii) \left(y-8\right)\times\left(3y-4\right)=y\left(3y-4\right)-8\left(3y-4\right)
= y\times3y-y\times4-8\times3y-8\times-4
= 3y^2-4y-24y+12
= 3y^2-28y+12
(iii) \left(2.5l\ -\ 0.5m\right)\times\left(2.5l+0.5m\right)
= 2.5l\times\left(2.5l+0.5m\right)-0.5m\times\left(2.5l+0.5m\right)
= 2.5l\times2.5l+0.5l\times0.5m-0.5m\times2.5l-0.5m\times0.5m
= 6.25l^2+1.25lm-1.25lm-0.25m^2
= 6.25l^2-0.25m^2
(iv) \left(a+3b\right)\times\left(x+5\right)=a\left(x+5\right)+3b\left(x+5\right)
= a\times x+a\times5+3b\times x+3b\times5
= ax + 5a + 3bx + 15b
(v) \left(2pq+3q^2\right)\left(3pq-2q^2\right)
= 2pq\times\left(3pq-2q^2\right)+3q^2\left(3pq-2q^2\right)
= 2pq\times3pq-2pq\times2q^2+3q^2\times3pq-3q^2\times2q^2
= 6p^2q^2-4pq^3+9pq^2-6q^4
= 6p^2q^2+5pq^3-6q^4
(vi) \left(\frac{3}{4}a^2+3b^2\right)\times4\left(a^2-\frac{2}{3}b^2\right)
= \left(\frac{3}{4}a^2+3b^2\right)\times\left(4a^2-\frac{8}{3}b^2\right)
= \frac{3}{4}a^2\times\left(4a^2-\frac{8}{3}b^2\right)+3b^2\times\left(4a^2-\frac{8}{3}b^2\right)
= \frac{3}{4}a^2\times4a^2-\frac{3}{4}a^2\times\frac{8}{3}b^2+3b^2\times4a^2-3b^2\times\frac{8}{3}b^2
= 3a^4-2a^2b^2+12a^2b^2-8b^4
= 3a^4+10a^2b^2-8b^4
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