Expanding squares

Japanese school year: Junior high 3

What you learn

Learn to expand expressions in the form of squared binomials efficiently using the square of a sum and difference formulas. This skill is frequently required in completing the square and solving quadratic equations. Understanding basic polynomial expansion through the distributive property beforehand will make this topic easier.

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Key points

Use this when expanding the square of a sum, $(a + b)^2$ . Along with the squared terms $a^2$ and $b^2$ , twice their product ( $2ab$ ) appears in the middle.

(a + b)^2 = a^2 + 2ab + b^2

Use this when expanding the square of a difference, $(a - b)^2$ . It has the same structure as the sum formula, except the middle term has a minus sign ( $-2ab$ ).

(a - b)^2 = a^2 - 2ab + b^2

When expanding $(a + b)^2$ , take care not to omit the middle term $2ab$ . A very common mistake is writing only $a^2 + b^2$ .

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Practice 1Coming soon