The elegant shortcut for multiplying binomials with opposite signs
In short: Master the difference of squares, a fundamental algebraic pattern that allows you to expand complex expressions instantly without tedious FOIL multiplication.
The difference of squares pattern identifies that multiplying the sum and difference of two terms, (a + b) and (a - b), always results in the difference of their squares: a² - b². This rule provides a streamlined method for expanding expressions like (x + 2)(x - 2) into x² - 4.
The pattern remains consistent regardless of the complexity of the terms involved. It can be applied to larger coefficients and higher exponents, such as expanding (3 + 5x⁴)(3 - 5x⁴) into 9 - 25x⁸ or handling variables with different powers like (3y² + 2y⁵)(3y² - 2y⁵) to reach 9y⁴ - 4y¹⁰.
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Sources
- Summary by Intellect · source: Polynomial special products: difference of squares | Algebra 2 | Khan Academy
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