Algebraic Expressions
ICSE Class 8 · Mathematics · Chapter 11
What this chapter covers
- Variables, constants and expressions
- Terms, factors and coefficients
- Like and unlike terms, and kinds of expressions
- Degree of an expression
- Addition of algebraic expressions
- Subtraction of algebraic expressions
- Common errors in algebra
- Multiplication of algebraic expressions
- Division of algebraic expressions
Key points
- A variable is a letter that can take different values; a constant has a fixed value.
- Terms are the parts of an expression separated by + and - signs; the sign belongs to the term.
- The coefficient of a term is its numerical factor with its sign; in this class all coefficients are integers.
- Like terms have the same letters with the same powers; only like terms can be added or subtracted.
- Expressions with one, two and three unlike terms are monomials, binomials and trinomials.
- The degree of a term is the sum of the powers of its letters; the degree of a polynomial is its highest term degree.
- To subtract, change the sign of every term of the expression being subtracted, then add.
- 2 + x ≠ 2x and 7x + y ≠ 7xy; substitute a small number to test any doubtful step.
- To multiply, multiply coefficients and add powers of the same letter: xm × xn = xm+n.
- Multiply a polynomial by a monomial, or by another polynomial, term by term using the distributive property.
- To divide, divide coefficients and subtract powers: xm ÷ xn = xm-n; divide every term of a polynomial.
- Check a division by multiplying the quotient by the divisor.
Questions answered
In the expression 5a2 - ab + 7b - 4, name the terms, the coefficient of ab and the constant term.
The terms are 5a2, -ab, 7b and -4. The coefficient of ab is -1. The constant term is -4.
Sort into like terms: 3xy, -2x2, 7yx, x2, 4x, -xy.
3xy, 7yx and -xy are like terms; -2x2 and x2 are like terms; 4x stands alone.
Is 4m + 2n - m a trinomial? Explain briefly.
No. After joining the like terms 4m and -m, it becomes 3m + 2n, which is a binomial.
Find the degree of 3x2y3 - 5xy + 9x4.
The terms have degrees 5, 2 and 4, so the degree is 5.
Add 6p - 3q + 2, -2p + 5q and p - q - 7.
(6 - 2 + 1)p + (-3 + 5 - 1)q + (2 - 7) = 5p + q - 5.
Subtract 4a2 - 2a + 1 from a2 + 3a - 5.
(a2 + 3a - 5) - (4a2 - 2a + 1) = -3a2 + 5a - 6.
A student wrote 3 + 4y = 7y. Explain the error using y = 2.
3 and 4y are unlike terms and cannot be joined. With y = 2, 3 + 4y = 11, but 7y = 14, so the two are not equal.
Multiply (-4a2b) × (3ab3).
-12a3b4.