Expand Using the Binomial Theorem (4x+2)^6

${(4 x + 2)}^{6}$

Step 1

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

$\sum_{k = 0}^{6} \frac{6!}{(6 - k)! k!} \cdot {(4 x)}^{6 - k} \cdot {(2)}^{k}$

Step 2

Expand the summation.

$\frac{6!}{(6 - 0)! 0!} \cdot {(4 x)}^{6 - 0} \cdot {(2)}^{0} + \frac{6!}{(6 - 1)! 1!} \cdot {(4 x)}^{6 - 1} \cdot {(2)}^{1} + \dots + \frac{6!}{(6 - 6)! 6!} \cdot {(4 x)}^{6 - 6} \cdot {(2)}^{6}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(4 x)}^{6} \cdot {(2)}^{0} + 6 \cdot {(4 x)}^{5} \cdot {(2)}^{1} + \dots + 1 \cdot {(4 x)}^{0} \cdot {(2)}^{6}$

Step 4

Simplify the polynomial result.

$4096 x^{6} + 12288 x^{5} + 15360 x^{4} + 10240 x^{3} + 3840 x^{2} + 768 x + 64$

Expand Using the Binomial Theorem (4x+2)^6

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