Algebra presents many unique challenges that a student will not have faced in earlier math classes. One such challenge is how to deal with unlike variables and the reduction in flexibility that results. For example, in the expression (3 + 2)^3, a student could easily reduce this to 5^3 before solving it. However, in the expression (x + 2)^3 such flexibility has disappeared. To simplify this expression, the student must be able to cube a binomial expression. Fortunately, binomials raised to powers follow a straightforward pattern.
Write the binomial expression to be cubed, such as "a + b," in parentheses followed by the power of three: (a + b)^3. This represents cubing the binomial; this will be the left side of the equation.
Cube "a" and place this on the right side of the equation. If "a" is a coefficient with a variable, then cube both the coefficient and the variable. For example, 2x becomes 8x^3, while 5x^2 becomes 125x^8.
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Square "a" and multiply the result by 3. Multiply that product by "b" and add this result to the right side of the equation. For example, if "a" is 2x and "b" is 5, the second term would be 2x * 2x * 3 * 5, or 60x^2. The right side of your equation so far would be 8x^3 + 60x^2.
Square "b" and multiply the result by 3. Multiply that product by "a" and add this result to the right portion of the equation. For example, if "a" is 2x and "b" is 5, the third term will be 5 * 5 * 3 * 2x, or 150x.
Add the cube of "b" to the right side. Continuing to follow the example from Steps 3 and 4, if "b" is 5, the last term is 125. Thus, (2x + 5)^3 = 8x^3 + 60x^2 + 150x + 125. Likewise, if the terms were the original "a" and "b," the entire binomial function cubed looks like (a + b)^3 = a^3 + 3ba^2 + 3ab^2 + b^3.