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Encapsulate
math

ALGEBRAIC ExPRESSIonS

A combination of constants and variables connected by the signs of mathematical operations is called an algebraic
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expression. For example, 3x + 5xy + 7; ab + bc + cd – a .
Terms, Factors and Coefficients Types of Algebraic Expressions
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Expression 7x y + 3xy + 8 Monomial: An expression having one term.
For example, 7x .
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2
Terms 7x y 3xy 8 Binomial: An expression having two terms.
[Variable term] [Variable term] [Constant term] For example, 3x + 2.

Factors 7 x x y 3 x y Trinomial: An expression having three
terms. For example, 9x + 7x + 1.
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3
[Coefficient [Coefficient
2
of 7x y] of 3xy] Polynomial: An expression having one or
more terms with non-zero coefficients.
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2
operations of Algebraic Expressions For example, ax + bx + cx + dx + e.
Addition Subtraction
While adding polynomials, first look for like terms While subtracting polynomials, change the sign of
and add them, then handle the unlike terms. each term of subtrahend and add the two polynomials.
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2 2
For example, 5ab + 4xy – 3ax + 2 For example, 3a – 4a b + 5b 4
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2 2
(+) – 3ab – 13xy + 7bx + 9 a – a b – b 4
–
+
+
2ab – 9xy – 3ax + 7bx + 11 2a – 3a b + 6b 4
2 2
4
Multiplication Division
• Product of two monomials = (Product of their • When we divide a polynomial by a monomial, we
numerical coefficients) × (Product of their divide each term of the polynomial by the monomial.
algebraic factors) • To divide a polynomial by a binomial or a polynomial,
• While multiplying two polynomials, each term we can use the long division method. For example,
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of the multiplicand is multiplied by each term x – 7x + 14
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3
of the multiplier. Like terms are then added to x – 1 x – 8x + 21x – 16
3
get the final product. For example, x – x 2
+
2
4x – 2x + 5 – – 7x + 21x – 16
2
× 2x + 3 – 7x + 7x
2
2
3
8x – 4x + 10x (Multiplying by 2x) + –
+ 12x – 6x + 15 (Multiplying by 3) 14x – 16
2
3
2
8x + 8x + 4x + 15 (Adding like terms) 14x – 14
– +
–2
Identity
An algebraic equation that is true for all values of its variable(s) in the equality is called an identity.
Following are the standard identities:
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1. (a + b) = a + 2ab + b 2 2. (a – b) = a – 2ab + b 2
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2
2

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3. (a + b)(a – b) = a – b 2 4. (x + a) (x + b) = x + (a + b)x + ab
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