Algebraic Expressions & Identities Test - 3

(i) Monomial is an algebraic expression consisting of one non-zero term(s) only.
a is a monomial in one variable a, 10ab² is a monomial in two variables a and b.

(ii) A monomial in variable x is an expression of the form CX^k, where C is a constant and k is a non-negative integer.
A Polynomial in x is a sum of finitely many monomials in x. In other words, it is an expression of the form: P(x) = a_nxⁿ +a_n−1 +···+a₁x + a₀.

(iii) Any two polynomials can be added, subtracted or multiplied, and the result will be a polynomial. When polynomials are added, subtracted, or multiplied, the result is another polynomial. When polynomials are divided, the result is a rational expression. Polynomials can be added under the associative law of addition.


(iv) Terms, factors, and coefficients make up mathematical expressions.
A mathematical expression contains numbers, variables, symbols, and operators connected by addition, subtraction, multiplication, and division. These parts are called terms.

In a mathematical expression, factors are parts of the expression that are connected by multiplication.

A coefficient is a number that is multiplied by a variable in a mathematical expression.

We have 4p + 5q = 24 and pq = 8

Squaring both sides,
(4p + 5q)² = (24)²
(4p)² + (5q)² + 2 (4p) (5q) = (24)²

16p² + 25q² + 40pq = 576
16p² + 25q² + 40 × 8 = 576

16p² + 25q² = 576 – 320
16p² + 25q² = 256