Simplifying Algebraic Expressions

GRE Quantitative · Axiom Academy

LESSON Simplifying Expressions Combine like terms, expand with the distributive property, and multiply binomials with FOIL 1. Like Terms Combine Into One Like terms share the same variable raised to the same exponent — only their coefficients differ. Sort terms into matching groups by variable/exponent, then just add the coefficients within each group. Sort by variable and exponent — same "bin," same term Add the coefficients in each bin to get the simplified sum 2. Distribute the Outer Factor Across Every Term The distributive property says a factor multiplying a sum in parentheses must multiply each term inside — not just the first one. Picture it as an area: a rectangle of width a split by the sum (b+c) has two pieces, and the total area is the sum of both. The whole rectangle's area equals its two piece-areas added together Expand 3(2x+5) : multiply 3 by 2x to get 6x , then multiply 3 by 5 to get 15 . Add the pieces: Multiplying two binomials is the same area idea, in two dimensions . Split a rectangle both horizontally (by a+b ) and vertically (by c+d ) and you get four smaller pieces — First, Outer, Inner, Last. Add all four areas and you've multiplied the binomials. Expand (x+2)(x+3) term by term, then combine the two middle (like) terms: Every algebra topic ahead — equations, inequalities, quadratics, systems — starts by simplifying an expression first. These three moves are the toolkit. Scroll up to revisit any step.

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