Finite Math Examples

${(1.5 x - 2.1 y)}^{14}$

Step 1

Use the binomial expansion theorem to find each term. The binomial theorem states ${(a + b)}^{n} = \sum_{k = 0}^{n} n C k \cdot (a^{n - k} b^{k})$ .

$\sum_{k = 0}^{14} \frac{14!}{(14 - k)! k!} \cdot {(1.5 x)}^{14 - k} \cdot {(- 2.1 y)}^{k}$

Step 2

Expand the summation.

$\frac{14!}{(14 - 0)! 0!} \cdot {(1.5 x)}^{14 - 0} \cdot {(- 2.1 y)}^{0} + \frac{14!}{(14 - 1)! 1!} \cdot {(1.5 x)}^{14 - 1} \cdot {(- 2.1 y)}^{1} + \dots + \frac{14!}{(14 - 14)! 14!} \cdot {(1.5 x)}^{14 - 14} \cdot {(- 2.1 y)}^{14}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(1.5 x)}^{14} \cdot {(- 2.1 y)}^{0} + 14 \cdot {(1.5 x)}^{13} \cdot {(- 2.1 y)}^{1} + \dots + 1 \cdot {(1.5 x)}^{0} \cdot {(- 2.1 y)}^{14}$

Step 4

Simplify the polynomial result.

$291.92926025 x^{14} - 5721.81350097 x^{13} y + 52068.50285888 x^{12} y^{2} - 291583.61600976 x^{11} y^{3} + 1122596.92163759 x^{10} y^{4} - 3143271.38058527 x^{9} y^{5} + 6600869.89922907 x^{8} y^{6} - 10561391.83876651 x^{7} y^{7} + 12937705.00248898 x^{6} y^{8} - 12075191.33565638 x^{5} y^{9} + 8452633.93495947 x^{4} y^{10} - 4303159.09416118 x^{3} y^{11} + 1506105.68295641 x^{2} y^{12} - 324391.99325215 x y^{13} + 32439.19932521 y^{14}$