Final Answer
$6x^2+19x+15$
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Step-by-step Solution
Problem to solve:
$\left(3x+5\right)\left(2x+3\right)$
Solving method
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 ($L\times L$):
- ($F\times F$) is $(3x)(2x)$
- ($O\times O$) is $(3x)(3)$
- ($I\times I$) is $(5)(2x)$
- ($L\times L$) is $(5)(3)$
Then, combine the four terms in a sum: $(F\times F) + (O\times O) + (I\times I) + (L\times L)$:
$3\cdot 2x\cdot x+3\cdot 3x+5\cdot 2x+5\cdot 3$
2
Multiply $3$ times $2$
$6x\cdot x+3\cdot 3x+5\cdot 2x+5\cdot 3$
3
Multiply $3$ times $3$
$6x\cdot x+9x+5\cdot 2x+5\cdot 3$
4
Multiply $5$ times $2$
$6x\cdot x+9x+10x+5\cdot 3$
5
Multiply $5$ times $3$
$6x\cdot x+9x+10x+15$
6
When multiplying two powers that have the same base ($x$), you can add the exponents
$6x^2+9x+10x+15$
7
Combining like terms $9x$ and $10x$
$6x^2+19x+15$
Final Answer
$6x^2+19x+15$
