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Exercise

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

Step-by-step Solution

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 exercise

$6x^2+19x+15$

Try other ways to solve this exercise

  • 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...
Can't find a method? Tell us so we can add it.

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

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$\left(6x-5\right)\left(2x+3\right)$

$4\left(4a+5\right)$

$\left(5x+2y\right)\left(5x-2y\right)$

$\left(2x+6\right)^2$

Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

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