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# Multiplying Polynomials Calculator

'**Multiplying Polynomials Calculator**' is an online tool that helps to calculate the product of two polynomials.

## What is Multiplying Polynomials Calculator?

Online Multiplying Polynomials Calculator helps you to calculate the product of two polynomials within a few seconds.

### Multiplying Polynomials Calculator

**NOTE:** Enter polynomials in terms of x and y only.

## How to Use Multiplying Polynomials Calculator?

Follow these steps which will help you to use the calculator.

**Step 1**: Enter the polynomial 1 and polynomial 2 in the given input box.**Step 2**: Click on "**Multiply**" to find the product of two polynomials.**Step 3**: Click on "**Reset**" to clear the field and find the product of two different polynomials.

## How to Find Multiplying Polynomials?

"A polynomial is defined as a type of expression in which the exponents of all variables should be a whole number. To multiply two polynomials, we have to carry out the multiplication process term-by-term.

Let's look at the solved example to understand briefly.

**Solved Examples on Multiplying Polynomials Calculator**

**Example 1:**

Find the product of 1 + 3y and 2y + y^{2}

**Solution: **

= (1 + 3y) (2y + y^{2})

= (1 × 2y) + (1 × y^{2}) + (3y × 2y) + (3y × y^{2})

= 2y + y^{2} + 6y^{2} + 3y^{3 }

= 2y + 7y^{2} + 3y^{3}

= y(2 +7y + 3y^{2})

Hence the product of two polynomials is y(2 +7y + 3y^{2}).

**Example 2:**

Find the product of 4x^{2} + 5x^{7} and x + 8x^{4}

**Solution: **

= (4x^{2} + 5x^{7}) (x + 8x^{4})

= (4x^{2} × x) + (4x^{2} × 8x^{4}) + (5x^{7} × x) + (5x^{7} × 8x^{4})

= 4x^{3} + 32x^{6} + 5x^{8} + 40x^{11 }

= x^{3}(4x +32x^{3} + 5x^{5 }+ 40x^{8})

Hence the product of two polynomials is x^{3}(4x +32x^{3} + 5x^{5 }+ 40x^{8}).

**Example 3:**

Find the product of x + 3xy^{2} and x^{2}y + xy^{3})

**Solution: **

= (x + 3xy^{2}) (x^{2}y + xy^{3})

= (x × x^{2}y) + (x × xy^{3}) + (3xy^{2} × x^{2}y) + (3xy^{2} × xy^{3})

= x^{3}y + x^{2}y^{3} + 3x^{3}y^{3} + 3x^{2}y^{5}

= x^{2}y(x + y^{2} + 3xy^{2} + 3y^{4})

Hence the product of two polynomials is x^{2}y(x + y^{2} + 3xy^{2} + 3y^{4}).

Now use the calculator to find out the product between the given polynomials:

1) 8x^{3} + 3 and 2y^{2} + x^{3}

2) 2x^{2} + y^{3} and 2y^{3} + x^{2}

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