Square of a Binomial
the sum of: the square of the first terms, twice the product of the middle two terms, and the square of the last term
The square of a binomial is a common algebraic expression that involves squaring a sum or difference of two terms. The term binomial refers to a polynomial with two terms.
The formula for squaring a binomial is:
(a + b)² = a² + 2ab + b² – Square of Sum
(a – b)² = a² – 2ab + b² – Square of Difference
These formulas can be remembered using the acronym FOIL (First, Outer, Inner, Last), which reminds us to multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms, before combining the results.
For example, to square the binomial (x + 3):
(x + 3)² = x² + 2(x)(3) + 3²
(x + 3)² = x² + 6x + 9
And to square the binomial (2a – 5):
(2a – 5)² = (2a)² – 2(2a)(5) + 5²
(2a – 5)² = 4a² – 20a + 25
In both cases, we have expanded the binomial using the appropriate formula, distributed any coefficients, and simplified the result to obtain a quadratic polynomial.
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