Question

Use Pascal’s Triangle to write out the expansion of (a+b)3 .(1 point) Responses a3b3+3a2b2+3ab+1 a cubed b cubed plus 3 a squared b squared plus 3 a b plus 1 a3+3a2b+3ab2+b3 a cubed plus 3 a squared b plus 3 a b squared plus b cubed a3+b3 a cubed plus b cubed a+3a2b+3a3b2+b3

Answer 1

To expand \((a+b)^3\) using Pascal’s Triangle, we first note the coefficients from the third row of Pascal's Triangle, which are \(1, 3, 3, 1\).

Using these coefficients, the expansion of \((a+b)^3\) can be written as:

\[
1 \cdot a^3 \cdot b^0 + 3 \cdot a^2 \cdot b^1 + 3 \cdot a^1 \cdot b^2 + 1 \cdot a^0 \cdot b^3
\]

This simplifies to:

\[
a^3 + 3a^2b + 3ab^2 + b^3
\]

Thus, the correct response is:

**a³ + 3a²b + 3ab² + b³**