Multiplication identities

Japanese school year: Junior high 3

What you learn

Learn how to expand algebraic expressions efficiently using fundamental multiplication formulas such as the product of binomials. This foundation ensures speed and accuracy in calculations and is vital for subsequent factoring. Having a good grasp of the distributive property of polynomials beforehand is highly recommended.

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Key points

This formula expands the product of two linear expressions sharing the variable $x$ . The coefficient of $x$ is the sum $(a + b)$ , and the constant term is the product $ab$ .

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

This general formula expands the product of any two linear expressions. The leading coefficient is $ac$ , the linear term coefficient is the sum of products $(ad + bc)$ , and the constant term is $bd$ .

(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd

These formulas expand the square of a sum or difference of two terms. Between the squared terms $a^2$ and $b^2$ , the middle cross term $\pm 2ab$ is twice their product.

(a + b)^2 = a^2 + 2ab + b^2, \quad (a - b)^2 = a^2 - 2ab + b^2

This formula expands the product of the sum and difference of the same two terms. The middle terms cancel out, leaving only the difference of squares, $a^2 - b^2$ .

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

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Practice 1Coming soon