Question

Show the complete binomial expansion of (4x + y) ^5 . (Using Pascals Triangle)

Answer 1

Pascal triagle for (4x + y) ^5 becomes

1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

So we will use 1 5 10 10 5 1.

The expansion becomes

`\begin{gathered} \mleft(4x+y\mright)^5=\mleft(4x\mright)^5+5\mleft(4x\mright)^4y+10\mleft(4x\mright)^3y^2+10\mleft(4x\mright)^2y^3+5\mleft(4x\mright)y^4+1y^5 \\ (4x+y)^5=1024x^5+5(4x)^4y+10(4x)^3y^2+10(4x)^2y^3+20xy^4+y^5 \end{gathered}`