Multiply polynomial $ \, \color{blue}{ 32x+26x+23x+22x+16x+12x+11x+10x+8x+7x+5x+4x+2x+x+1 } \, $ by $ \, \color{orangered}{ 2x+5 }$.

$$ \left( \color{blue}{32x+26x+23x+22x+16x+12x+11x+10x+8x+7x+5x+4x+2x+x+1} \right) \cdot \left( \color{orangered}{2x+5} \right) = 358x^2+897x+5 $$

Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= 179x+1 \\ Q(x) &= 2x+5 \\ \end{aligned} $$

In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ 179x+1}\right) \cdot \left( \color{orangered}{ 2x+5}\right) &= \underbrace{ \color{blue}{179x} \cdot \color{orangered}{2x} }_{\text{FIRST}} + \underbrace{ \color{blue}{179x} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{2x} }_{\text{INNER}} + \underbrace{ \color{blue}{1} \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= 358x^2 + 895x + 2x + 5 = \\ &= 358x^2 + 895x + 2x + 5 = \\ &= 358x^2+897x+5; \end{aligned} $$

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