Square of a Binomial Calculator

A binomial is a polynomial with two terms, such as (a + b) or (c - d). When you square a binomial, you are multiplying the expression by itself. Rather than performing long multiplication or FOIL (First, Outer, Inner, Last) every time, algebraic shortcuts known as special products are applied. For a sum of two terms, the formula is (a + b)^2 = a^2 + 2ab + b^2. For a difference of two terms, the formula is (c - d)^2 = c^2 - 2cd + d^2. The resulting expression is always a trinomial, specifically called a perfect square trinomial.

Let us walk through squaring the binomial sum (3x + 5)^2. Here, our first term (a) is 3x, and our second term (b) is 5. Step 1: Square the first term, giving (3x)^2 = 9x^2. Step 2: Multiply the two terms together and double the product, yielding 2 * (3x) * (5) = 30x. Step 3: Square the second term, resulting in 5^2 = 25. Combining these parts using the sum formula gives us the final expanded expression: 9x^2 + 30x + 25.

Always pay close attention to the middle sign. A common mistake is turning the middle term negative when squaring a binomial sum. Remember that the final term in both sum and difference expansions is always positive because squaring any non-zero real number yields a positive result. When working with variables and coefficients, apply the exponent to both the numerical coefficient and the variable part during the first and last steps.