Rev. Exr 4-Class 9th (P. Board)-Ytb

Algebraic Expressions And Algebraic Formulas:

The following topics have been discussed in Chapter – 4.

• Algebraic Expressions
• Algebraic Formula
• Surds and their Application
• Rationalization
• Algebraic Expressions: Arithmetic is generalized in the subject of Algebra. Algebraic Terms, when subject to subtraction and/or additions, we get Algebraic Expressions. The following are some examples of Algebraic Expressions:

8 X3 + 5 Y2,

5 a + 3bc +8b

4p2 – 9q2 + 3pq

Polynomials:

An Agebraic Expression of the form

P (x) = an xn +an-1 xn-1 + an-2 xn-2 + . . . . + a1 x + a0      where an is not equal to zero.

Degree of Polynomial: Degree of Polynomial is n when it has the highest power of x and is a non-negative integer.

Leading Coefficient of the Polynomial:           The Coefficient  an of the highest power of x is called the leading coefficient.

The Algebraic Expression:   2 x4 y3 + x2y2 + 8x is a Polynomial of two variables x and y and has degree 7.

Rational Expressions Behave like Rational Numbers

Rational Expression:

The quotient of two polynomials p(x) and q(x), p(x)/q(x), where q(x) is not zero, is called a Rational Expression. Every polynomial can be considered as a Rational Expression but every Rational Expression is not necessarily a Polynomial.

Rational Expression in its Lowest Form:       When two Polynomials p(x) and q(x) with integral coefficients have no common factor, the rational expression p(x)/q(x), is said to be in its lowest form.

Working Rules to Reduce the Rational Expression to its Lowest Form:

• Make factors of each polynomial p(x) and q(x)
• Find H.C.F. of p(x) and q(x)
• Divide the numerator and the denominator by H.C.F.

The Rational Expression so obtained is in its lowest form.

Evaluation of Algebraic Expression at some particular Real Number:

When we substitute the variables with their specific values, the resulting number is the value of that Algebraic Expression.

Surds and their Application:     An irrational radical with rational radicand is called a Surd.

Addition and Subtraction of Surds:    Similar Surds, having the same irrational factors, can be added to make a single term.

Multiplication and Division of Surds: Surds of the same order can be multiplied and divided.

Rationalization of Surds:

• A Surd which contains a single term is called a monomial surd.
• A Surd which contains a sum of two monomial surds or one monomial surd and a rational number is called a binomial surd.
• When the product of the of two surds is a rational number, the each surd will be the rationalizing factor of the other.
• When a surd is multiplied by its rationalizing factor, we get a rational number. The process is called Rationalization of the given surd.

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