"Question 1 Multiply the binomials. (i) (2x + 5) and (4x − 3) (ii) (y − 8) and (3y − 4) (iii) (2.5l − 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5) (v) (2pq + 3q^2) and (3pq − 2q^2) (vi) 3a^2/4 + 3b^2
Class 8 Algebraic Expressions and Identities Page 148"
Answers
Algebraic expressions:
A combination of constants and variables connected by any or all of the four fundamental operations +, -,×,÷ is called an algebraic expression
Multiplication of algebraic expression:
The product of two factors with like signs is positive and the product of two factors with unlike signs is negative.
Multiplication of a binomial and the binomial:
Let ( a+b)& (c+d) are two Binomials. By using distributive law of multiplatinum over addition twice, we may find their product
( a+b)× (c+d)
= a(c+d) + b( c+d)
=(a × c+a × d)+(b × c+b × d)
= ac+ad+bc+bd
This
method is known as the horizontal method.
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Solution:
i)
(2x + 5)(4x - 3)
2x(4x - 3)+ 5 (4x-3)
= 2x x 4x - 2x x 3 + 5 x 4x - 5 x 3
= 8x² - 6x + 20x -15
= 8x² + 14x -15
ii) ( y - 8)(3y - 4)
y(3y - 4)-8(3y - 4)
= y x 3y - 4y - 8 x 3y + 32
= 3y² - 4y - 24y + 32
= 3y² - 28y + 32
iii) (2.5l - 0.5m)(2.5l + 0.5m)
2.5l (2.5l + 0.5m) -0.5m(2.5l + 0.5m)
= 2.5l × 2.5l + 2.5l ×0.5m -0.5m× 2.5l + 0.5m× 0.5m
= 6.25l² +1.25lm – 1.25lm + 0.25n²
= 6.25l² - 0.25m²
iv)( a+3b)(x+5)
a(x+5)+3b(x+5)
ax + 5a + 3b x + 15b
v) (2pq+3q²)(3pq-2q²)
2pq(3pq-2q²) + 3q²(3pq-2q²)
2pq x 3pq - 2pq x 2q² + 3q²x 3pq - 3q2 x 2q²
= 6p²q² - 4pq³ + 9pq³- 6q⁴
= 6p²q² + 5pq³ - 6p⁴
vi) ( 3a²/4+3b²)(4(a² -2b²/3))
( 3a²/4+3b²)(4a² -8b²/3)
=3a²/4((4a² -8b²/3)+ 3b²(4a² -8b²/3)
= 3a⁴-2a²b²+12a²b²-8b⁴
= 3a⁴+10a²b²-8b⁴
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