Finite Math Examples

${(A + B)}^{2}$

Step 1

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

$\sum_{k = 0}^{2} \frac{2!}{(2 - k)! k!} \cdot {(A)}^{2 - k} \cdot {(B)}^{k}$

Step 2

Expand the summation.

$\frac{2!}{(2 - 0)! 0!} {(A)}^{2 - 0} \cdot {(B)}^{0} + \frac{2!}{(2 - 1)! 1!} {(A)}^{2 - 1} \cdot {(B)}^{1} + \frac{2!}{(2 - 2)! 2!} {(A)}^{2 - 2} \cdot {(B)}^{2}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(A)}^{2} \cdot {(B)}^{0} + 2 \cdot {(A)}^{1} \cdot {(B)}^{1} + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4

Simplify each term.

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Step 4.1

Multiply ${(A)}^{2}$ by $1$ .

${(A)}^{2} \cdot {(B)}^{0} + 2 \cdot {(A)}^{1} \cdot {(B)}^{1} + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4.2

Anything raised to $0$ is $1$ .

$A^{2} \cdot 1 + 2 \cdot {(A)}^{1} \cdot {(B)}^{1} + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4.3

Multiply $A^{2}$ by $1$ .

$A^{2} + 2 \cdot {(A)}^{1} \cdot {(B)}^{1} + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4.4

Simplify.

$A^{2} + 2 \cdot A \cdot {(B)}^{1} + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4.5

Simplify.

$A^{2} + 2 A \cdot B + 1 \cdot {(A)}^{0} \cdot {(B)}^{2}$

Step 4.6

Multiply ${(A)}^{0}$ by $1$ .

$A^{2} + 2 A B + {(A)}^{0} \cdot {(B)}^{2}$

Step 4.7

Anything raised to $0$ is $1$ .

$A^{2} + 2 A B + 1 \cdot {(B)}^{2}$

Step 4.8

Multiply ${(B)}^{2}$ by $1$ .

$A^{2} + 2 A B + B^{2}$