Step-by-step Solution

Expand the expression $\left(3x+5\right)\left(2x+3\right)$

Go!
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Final Answer

$19x+6x^2+15$

Step-by-step explanation

Problem to solve:

$\left(3x+5\right)\left(2x+3\right)$

Choose the 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

Adding $9x$ and $10x$

$x\left(9+10\right)+6x^2+15$
8

Add the values $9$ and $10$

$19x+6x^2+15$

Final Answer

$19x+6x^2+15$
$\left(3x+5\right)\left(2x+3\right)$

Main topic:

Special products

Steps:

8

Time to solve it:

~ 0.06 s (SnapXam)

Related topics:

Special productsFOIL Method