Expand any binomial of the form (ax + by)ⁿ where a and b can be any real numbers (integers, decimals).
Enter expression with EXACTLY TWO TERMS (degree 1 monomials) and power to see detailed expansion
The binomial theorem applies ONLY to expressions with exactly two terms: \[ (x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k \] where the binomial coefficient \(\displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)!}\).
Example 1: \((2.5x + 1.5y)^3\)
\[ \begin{aligned} (2.5x + 1.5y)^3 &= \sum_{k=0}^{3} \binom{3}{k} (2.5x)^{3-k} (1.5y)^k \\ &= 15.625x^3 + 28.125x^2y + 16.875xy^2 + 3.375y^3 \end{aligned} \]
ax + by where a and b can be any real numbers.x, y, a, b).- for subtraction, + for addition. Do not use spaces.
[1] Swokowski, Cole. Algebra and Trigonometry, 1997. ISBN: 0-534-95308-5
[2] Larson, Hostetler, Edwards, Heyd. Algebra and Trigonometry with Analytic Geometry, 1997. ISBN: 0-669-41723-8