Expand the expression (0.1x^2+3)(2.5x^2+3)

 Exercise

$\left(0.1x^2+3\right)\left(2.5x^2+3\right)$

 

Multiply the single term $2.5x^2+3$ by each term of the polynomial $\left(0.1x^2+3\right)$

$0.1x^2\left(2.5x^2+3\right)+3\left(2.5x^2+3\right)$

 

Multiply the single term $0.1x^2$ by each term of the polynomial $\left(2.5x^2+3\right)$

$0.25x^2\cdot x^2+0.3x^2+3\left(2.5x^2+3\right)$

 

When multiplying exponents with same base we can add the exponents

$0.25x^{4}+0.3x^2+3\left(2.5x^2+3\right)$

 

Multiply the single term $3$ by each term of the polynomial $\left(2.5x^2+3\right)$

$0.25x^{4}+0.3x^2+7.5x^2+9$

 

Combining like terms $0.3x^2$ and $7.5x^2$

$0.25x^{4}+7.8x^2+9$

$0.25x^{4}+7.8x^2+9$

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