Product of a sum and a difference

Japanese school year: Junior high 3

What you learn

Learn the formula for expanding the product of the sum and difference of two terms into a difference of squares. This formula simplifies algebraic manipulation and is crucial for rationalizing denominators later on. Being comfortable with operations on positive and negative numbers and basic polynomial multiplication is beneficial.

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Key points

Use this when multiplying the sum and difference of the same two terms, $a$ and $b$ . The middle terms cancel each other out, leaving the difference of their squares, $a^2 - b^2$ .

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

Use this when multiplying the sum and difference of two square roots, $\sqrt{a}$ and $\sqrt{b}$ . Squaring both terms removes the radicals, yielding $a - b$ , which is useful for rationalizing denominators.

(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a - b \quad (a > 0, \; b > 0)

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Practice 1Coming soon