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Polynomials Calculator

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1

Solved example of polynomials

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

We can multiply the polynomials $\left(6x-5\right)\left(2x+3\right)$ 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 $(6x)(2x)$
  • ($O\times O$) is $(6x)(3)$
  • ($I\times I$) is $(-5)(2x)$
  • ($L\times L$) is $(-5)(3)$

Then, combine the four terms in a sum: $(F\times F) + (O\times O) + (I\times I) + (L\times L)$:

$6\cdot 2x\cdot x+6\cdot 3x-5\cdot 2x-5\cdot 3$
3

Multiply $6$ times $2$

$12x\cdot x+6\cdot 3x-5\cdot 2x-5\cdot 3$
4

Multiply $6$ times $3$

$12x\cdot x+18x-5\cdot 2x-5\cdot 3$
5

Multiply $-5$ times $2$

$12x\cdot x+18x-10x-5\cdot 3$
6

Multiply $-5$ times $3$

$12x\cdot x+18x-10x-15$
7

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

$12x^2+18x-10x-15$
8

Combining like terms $18x$ and $-10x$

$12x^2+8x-15$

Final Answer

$12x^2+8x-15$

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