# Step-by-step Solution

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

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### Videos

$6x^2+19x+15$

## Step-by-step Solution

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

Combining like terms $9x$ and $10x$

$6x\cdot x+19x+15$
7

When multiplying two powers that have the same base ($x$), you can add the exponents

$6x^2+19x+15$

$6x^2+19x+15$
SnapXam A2

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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