How do you get the cube of a binomial?
For cubing a binomial we need to know the formulas for the sum of cubes and the difference of cubes.
Sum of cubes:
The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.
(a + b)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}Difference of cubes:
The difference of a cubed of two binomial is equal to the cube of the first term, minus three times the square of the first term by the second term, plus three times the first term by the square of the second term, minus the cube of the second term.
Workedout examples for the expansion of cube of a binomial:
Simplify the following by cubing:
1. (x + 5y)^{3} + (x – 5y)^{3}
2. \((\frac{1}{2} x + \frac{3}{2} y)^{3} + (\frac{1}{2} x  \frac{3}{2} y)^{3}\)
Solution:
Here a = \(\frac{1}{2} x, b = \frac{3}{2} y\)
\(=(\frac{1}{2} x)^{3} + 3\cdot (\frac{1}{2} x)^{2} \cdot \frac{3}{2} y + 3 \cdot \frac{1}{2} x \cdot (\frac{3}{2}y)^{2} + (\frac{3}{2}y)^{3} + (\frac{1}{2} x)^{3}  3\cdot (\frac{1}{2} x)^{2} \cdot \frac{3}{2} y + 3 \cdot \frac{1}{2} x \cdot (\frac{3}{2}y)^{2}  (\frac{3}{2}y)^{3}\)
\(=\frac{1}{8} x^{3} + \frac{9}{8} x^{2} y + \frac{27}{8} x y^{2} + \frac{27}{8} y^{3} + \frac{1}{8} x^{3}  \frac{9}{8} x^{2} y + \frac{27}{8} x y^{2}  \frac{27}{8} y^{3}\)
\(=\frac{1}{8} x^{3} + \frac{1}{8} x^{3} + \frac{27}{8} x y^{2} + \frac{27}{8} x y^{2}\)
\(=\frac{1}{4} x^{3} + \frac{27}{4} x y^{2} \)
Therefore, \[(\frac{1}{2} x + \frac{3}{2} y)^{3} + (\frac{1}{2} x  \frac{3}{2} y)^{3} = \frac{1}{4} x^{3} + \frac{27}{4} x y^{2} \]
The steps to find the mixed problem on cube of a binomial will help us to expand the sum or difference of two cubes.
`7th Grade Math Problems
8th Grade Math Practice
From Cube of a Binomial to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.