"Question 4 (a) Simplify 3x (4x −5) + 3 and find its values for (i) x = 3, (ii) . (b) a (a^2 + a + 1) + 5 and find its values for (i) a = 0, (ii) a = 1, (iii) a = − 1.
Class 8 Algebraic Expressions and Identities Page 146"
Answers
Algebraic expressions:
A combination of constants and variables connected by any or all of the four fundamental operations +, -,×,÷ is called an algebraic expression.
Terms:
The different parts of the expression separated by the sign+ or – are called the terms of the 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 monomial and the binomial:
If P, q & r are the three monomials we use the distributive law.
p×(q+r)= p×q+ p×r
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Solution:
a)3x (4x −5) + 3
(3x x 4x )- (3x x 5) +3
12x² -15x +3
i) Putting x=3 in the equation we get
12x² - 15x + 3
= 12(3)²-15(3)+3
= 12×9 -45+3
=108-45+3 = 66
(ii) putting x=1/2 in the equation we get
12x² - 15x + 3
12(1/2)² - 15 (1/2) +3
12×1/4 – 15/2+3
12/4 -15/2+3
3-15/2+3
3+3-15/2
6-15/2 =( 12-15)/2
= -3/2
b)
a(a²+a+1) +5
=a³+a²+a +5
(i) putting a= 0 in the equation we get
a³+a²+a +5
0³+0²+0+5 =5
(ii) putting a=1 in the equation we get
a³+a²+a +5
1³ + 1² + 1 +5
= 1 + 1 + 1 +5= 8
(iii) Putting a = -1 in the equation we get
a³+a²+a +5
-1³+1² -1+5
= -1 + 1 -1+5 = 4
==========================================================Hope this will help you....
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3x(4x−5)+3=12x^2−15x+3
x=3 gives the value 12(9)−15×3+3
=108−45+3
=66
x=1/2 gives the value 12(1/4)−15×(1/2)+3
=3−7.5+3
= - 3/2