"Question 1 Carry out the multiplication of the expressions in each of the following pairs. (i) 4p, q + r (ii) ab, a − b (iii) a + b, 7a^2b^2 (iv) a^2 − 9, 4a (v) pq + qr + rp, 0
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.
Monomials:
A monomial is a one term 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 monomial and the binomial:
If P, q & r are the three monomials we use the distributive law.
p×(q+r)= p×q+ p×r
=========================================================
Solution:
i)4p, q + r
4p(q + r) = (4p x q) + (4p x r )
=4pq + 4pr
ii)ab, a − b
ab(a - b) = = (ab x a) + (ab x -a)
=a²b - ab²
iii) a + b, 7a²b²
(a + b) (7a²b²) = ( a x 7a²b²) + (b x 7a²b²)
=7a³b²+ 7a²b³
iv) a²− 9, 4a
(a² - 9)(4a) = (a² x 4a) + ( -9 x 4a)
= 4a³ - 36a
v) pq + qr + rp, 0
(pq + qr + rp) x 0 = (pq x 0) + (qr x 0) + (rp x 0)
= 0
==========================================================
Hope this will help you....
Step-by-step explanation:
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.
Monomials:
A monomial is a one term 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 monomial and the
binomial:
If P, q & r are the three monomials we
use the distributive law.
p×(q+r)= p×q+ p×r
=========================================================
Solution:
i)4p, q + r
4p(q + r) = (4p x q) + (4p x r )
=4pq + 4pr
ii)ab, a − b
ab(a - b) = = (ab x a) + (ab x -a)
=a²b - ab²
iii) a + b, 7a²b²
(a + b) (7a²b²) = ( a x 7a²b²) + (b x 7a²b²)
=7a³b²+ 7a²b³
iv) a²− 9, 4a
(a² - 9)(4a) = (a² x 4a) + ( -9 x 4a)
= 4a³ - 36a
v) pq + qr + rp, 0
(pq + qr + rp) x 0 = (pq x 0) + (qr x 0) + (rp x 0)
= 0
==========================================================
Hope this will help you....