Algebra Play

Overview

This chapter works with algebraic expressions and identities: adding, subtracting and multiplying expressions, and using standard identities to expand and simplify. Algebra generalises arithmetic using letters for numbers.

Key concepts

• A term is a product of numbers and variables; like terms have the same variable parts.
• Only like terms can be added or subtracted.
• Monomial, binomial and trinomial have one, two and three terms.
• An identity is true for all values of the variables.

Important formulae

• (a + b)² = a² + 2ab + b²
• (a − b)² = a² − 2ab + b²
• (a + b)(a − b) = a² − b²

Solved example

1. Find 102² using an identity.
2. Write 102 = 100 + 2, so 102² = (100 + 2)².
3. = 100² + 2(100)(2) + 2² = 10000 + 400 + 4 = 10404.

Important questions

1. Simplify 5x + 3y − 2x + 7y.
2. Expand (2a + 3b)².
3. Use an identity to evaluate 98 × 102.
4. Multiply (x + 4)(x − 4) and state which identity you used.

Quick revision

Combine only like terms. Memorise the three standard identities — they speed up squaring numbers and multiplying special pairs. The product (a + b)(a − b) instantly gives a difference of squares.