Question

Complete the expansion of (a + b)6 with a = 1 and b = 0.3.

Answer 1

Answer:

$(1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}$

Step-by-step explanation:

This is an expansion of the expression $(a+b)^{6}$. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that

$(a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}$

Where the coeficients $n\choose k$ are called binomial coeficients, and can be computed by the formula

${n\choose k} =\frac{n!}{(n-k)! k!}$

where $n!=1\times 2\times 3\times \cdots\times n$.

Answer 2

(1+0.3)^6=(1)^6+6(1)^5(0.3)+15(1)^4(0.3)^2+20(1)^3(0.3)^3+15(1)^2(0.3)^4+6(1)(0.3)^5+(0.3)^6

(1+0.3)^6=1+6(1)(0.3)+15(1)(0.09)+20(1)(0.027)+15(1)(0.0081)+6(0.00243)+0.000729

(1+0.3)^6=1+1.8+1.35+0.54+0.1215+0.01458+0.000729