Final answer to the problem
$6x^2+19x+15$
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Step-by-step Solution
How should I solve this problem?
- FOIL Method
- Product of Binomials with Common Term
- Find the integral
- Find the derivative
- Factor
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Load more...
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1
We can multiply the polynomials $\left(3x+5\right)\left(2x+3\right)$ by using the FOIL method. The acronym F O I L stands for multiplying the terms in each bracket in the following order: First by First ($F\times F$), Outer by Outer ($O\times O$), Inner by Inner ($I\times I$), Last by Last ($L\times L$)
$\begin{matrix}(F\times F)\:=\:(3x)(2x)\\(O\times O)\:=\:(3x)(3)\\(I\times I)\:=\:(5)(2x)\\(L\times L)\:=\:(5)(3)\end{matrix}$
2
Then, combine the four terms in a sum
$(F\times F) + (O\times O) + (I\times I) + (L\times L)$
3
Substitute the values of the products
$3x2x+3\cdot 3x+5\cdot 2x+5\cdot 3$
4
Multiply $5$ times $3$
$3\cdot 2x\cdot x+3\cdot 3x+5\cdot 2x+15$
5
Multiply $3$ times $2$
$6x\cdot x+3\cdot 3x+5\cdot 2x+15$
6
Multiply $3$ times $3$
$6x\cdot x+9x+5\cdot 2x+15$
7
Multiply $5$ times $2$
$6x\cdot x+9x+10x+15$
8
Combining like terms $9x$ and $10x$
$6x\cdot x+19x+15$
9
When multiplying two powers that have the same base ($x$), you can add the exponents
$6x^2+19x+15$
Final answer to the problem
$6x^2+19x+15$
