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

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asin
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asinh
acosh
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##  Final answer to the problem

$6x^2+19x+15$
Got another answer? Verify it here!

##  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
Can't find a method? Tell us so we can add it.
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 ($L\times L$)

$\begin{matrix}(F\times F)\:=\:(3x)(2x)\\(O\times O)\:=\:(3x)(3)\\(I\times I)\:=\:(5)(2x)\\(L\times L)\:=\:(5)(3)\end{matrix}$
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Then, combine the four terms in a sum

$(F\times F) + (O\times O) + (I\times I) + (L\times L)$
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Substitute the values of the products

$3x2x+3\cdot 3x+5\cdot 2x+5\cdot 3$
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Multiply $5$ times $3$

$3\cdot 2x\cdot x+3\cdot 3x+5\cdot 2x+15$
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Multiply $3$ times $2$

$6x\cdot x+3\cdot 3x+5\cdot 2x+15$
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Multiply $3$ times $3$

$6x\cdot x+9x+5\cdot 2x+15$
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Multiply $5$ times $2$

$6x\cdot x+9x+10x+15$
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Combining like terms $9x$ and $10x$

$6x\cdot x+19x+15$
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When multiplying two powers that have the same base ($x$), you can add the exponents

$6x^2+19x+15$

##  Final answer to the problem

$6x^2+19x+15$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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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

###  Main Topic: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.