NCERT Solutions for Class 7 Maths Chapter 12 Exercise 12.3

We have:
(i) 6ab x 4b = (6 x 4) x (a x b x b) = 24ab¹⁺¹ = 24ab²
(ii) 5ab² c³ x 7a² b c = (5 x 7) x (a x a² x b² x b x c³ x c)
= 35 x a¹⁺² x b²⁺¹ x c³⁺¹ = 35 a³ b³ c⁴
(iii) -6x² yz by 2/3 xy³ z² = – 6 x 2/3 x (x² X x X y X y³ x z X z²)
= -4 X x²⁺¹ y³⁺¹ X z¹⁺² = – 4x³ y4 z³

We have:
(i) -8ab² c X 3a² b X -1/6 = -8 X 3 X -1/6 (a X a² X b² X b X c)
= 4 X (a¹⁺² X b²⁺¹ X c)
= 4 a³ b³ c
(ii) (5/8) a³ b², 12a² b and 6c
= (5/8) X 12 X 6 (a³ X a² X b² X b X 6c)
= 45 a⁵ b³ c

The multiplication/division rule for equations tell us that every term on both sides of an equation can be multiplied or divided by the same term (except zero) without changing the solution set of the equation.

Most of the times, physical and chemical sciences employ the basics of algebraic equations. In the case of computer sciences, the algorithms are based on the algebraic operations only. Moreover, algebra is involved in the field of art and architecture to calculate correct proportions so as to put forth a masterpiece.

Here are the basic steps to follow to simplify an algebraic expression:
(i) Remove parentheses by multiplying factors.
(ii) Use exponent rules to remove parentheses in terms with exponents.
(iii) Combine like terms by adding coefficients.
(iv) Combine the constants.