Algebraic Expressions and Formulas

Mathematics — First Preparatory

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Simplify 5x + 3y − 2x + 4y	Simplify
Solution	Add the like terms: (5x − 2x) + (3y + 4y) = 3x + 7y	liketerms
Example 2	Simplify 2(3a − 4) − (a + 5)	Simplify
Solution	6a − 8 − a − 5 = 5a − 13
Example 3	Find the value of 3x² − 2xy + y when x = 2 and y = −1	Findvalue
Solution	3 × 2² = 12 −2 × 2 × (−1) = 4 and y = −1. The value is 12 + 4 − 1 = 15	value
Example 4	Write an expression for “a number increased by 7 then the result multiplied by 3”	Writeexpressionnumberincreased
Solution	Let the number be x. The expression is 3(x + 7). If x = 5 the value is 3 × 12 = 36	numberexpressionvalue
Example 5 (the hardest)	Simplify 4(2x − y) − 3(x − 2y)	Simplify
Solution	8x − 4y − 3x + 6y = 5x + 2y

Algebraic Expressions and Formulas · 4 / 6