Question

Multiply the polynomials.
(3x2 + 4x + 4)(x-4)

Answer 1

Multiplication of two polynomials
`\left(3 x^(2)+4 x+4\right) \text { and }(x-4) \text { is } 3 x^(3)-8 x^(2)-12 x-16`

Solution:

Need to multiply following polynomial

`\left(3 x^(2)+4 x+4\right)(x-4)`

`\text { Lets for sake of simplicity }\left(3 x^(2)+4 x+4\right)=\mathrm{A}`

`\text { So }\left(3 x^(2)+4 x+4\right) *(x-4)=\mathrm{A} *(x-4)=\mathrm{A} *(x)-\mathrm{A} * 4`

`\text { Now again substitute value of } \mathrm{A} \text { as }\left(3 x^(2)+4 x+4\right)`

`=>\left(3 x^(2)+4 x+4\right) *(x-4)=\left[\left(3 x^(2)+4 x+4\right) *(x)\right]-\left[\left(3 x^(2)+4 x+4\right) * 4\right]`

On opening the internal brackets we get,

`\begin{array}{l}{\Rightarrow\left(3 x^(2)+4 x+4\right) * (x-4)=\left[3 x^(3)+4 x^(2)+4 x\right]-\left[12 x^(2)+16 x+16\right]} \\\\ {\Rightarrow\left(3 x^(2)+4 x+4\right) * (x-4)=3 x^(3)+4 x^(2)+4 x-12 x^(2)-16 x-16}\end{array}`

On bringing similar terms together, we get

`\begin{array}{l}{=>\left(3 x^(2)+4 x+4\right) * (x-4)=3 x^(3)+4 x^(2)-12 x^(2)+4 x-16 x-16} \\ {=>\left(3 x^(2)+4 x+4\right) * (x-4)=3 x^(3)-8 x^(2)-12x-16}\end{array}`

Hence the product is found out