Param Publication

Multiplication of algebraic expressions
Following rules of signs and the laws of exponents used in multiplication.

1.     Rules of signs in multiplication :
The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative. Thus if a and b are two positive numbers then 2.    Laws of exponents in multiplication
Law of exponents in multiplication is given as :
am x an  = am+n  x e.g. x5 x x2 = x5 + 2 = x7

Multiplication of a Monomial by a Monomial : Thus in multiplication of algebraic expression :
(i)     Write the product of the numerical coefficients.
(ii)     Write all the different letters occurring in the algebraic expressions giving to each letter an exponent (power) equal to the sum of all the exponents of that letter in the given expressions.
(iii)     The sign of the product is minus if there is an odd number of negative factors and plus if there is an even number of negative factors.

Multiplication of a Binomial by a Monomial :
In order to multiply a binomial by a monomial use the following rule :
a x (b + c)  = a x b + a x c.

Illustration
Multiply  : (i)   3x2 + 4xy by 2x         (ii) –4a [a + 3b]    (iii) – 4a [a – 3b]
Solution
(i)     2x [3x2 + 4xy] = 2x x 3x2 + 2x x 4xy  = 6x3 + 8x2
(ii)     – 4a [a + 3b]  = – 4a x a  – 4a x 3b = – 4a2 – 12ab
(iii)     – 4a [a – 3b] = – 4a ´ a – 4a ´ (–3b) = – 4a2 + 12 ab.

Multiplication of a Binomial by a Binomial :
In multiplication of a binomial by binomial we will use the law of multiplication of a binomial by a monomial twice.
Illustration
(i)     (a + b) (c + d)
(ii)     (2x2 + 3y) (3x2 – 2y)
Solution
(i)     (a + b) (c + d)     = a (c + d) + b (c + d)
= a x c + a x d + b x c + b x d
= ac + ad + bc + bd

(ii)     (2x2 + 3y) (3x2 – 2y)
= 2x2 (3x2 – 2y) + 3y (3x2 – 2y)
= 2x2 x 3x2 + 2x2 x (– 2y) + 3y x 3x2 + 3y x (–2y)
= 6x4 – 4x2y + 9x2y – 6y2

LIVE MATHS FOR CLASS 7

EDUCARE

Course : CBSE Class 7

Start Date : 26.01.2022

End Date : 03.03.2022

Types of Batch : Live Online Class

 Subject M T W T F S S Mathematics(120 hours) 7:00 PM 7:00 PM 7:00 PM 7:00 PM 7:00 PM - - 