# Multiplying Polynomials Calculator with steps | Polynomial multiplier

## Multiplying Polynomials Calculator

Enter a mathematical expression... #### Oh snap!

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Our Multiplying Polynomials Calculator with Steps is designed to help you solve polynomial multiplication problems with ease and precision. Our user-friendly interface and step-by-step guidance make it easy for anyone to solve even the most complex polynomial multiplication problems.

Follow these instructions to use our Polynomial multiplier:

1. Enter the polynomial expressions you want to multiply in the input fields.
2. Use the ^ symbol to indicate exponents and the * symbol for multiplication.
3. Click the “Calculate” button to get the result. The solution will be displayed along with a step by step guide on how to obtain it.
4. If you want to start again, please click the “x” button to return to the main interface.
Valid functions and symbols Description
sqrt() Square root
ln() Natural logarithm
log() Logarithm base 10
^ Exponents
abs() Absolute value
sin(), cos(), tan(), csc(), sec(), cot() Basic trigonometric functions
asin(), acos(), atan(), acsc(), asec(), acot() Inverse trigonometric functions
sinh(), cosh(), tanh(), csch(), sech(), coth() Hyperbolic functions
asinh(), acosh(), atanh(), acsch(), asech(), acoth() Inverse hyperbolic functions
pi PI number (π = 3.14159...)
e Neper number (e= 2.71828...)
i To indicate the imaginary component of a complex number.

Table 1: Valid functions and symbols

## How to multiply polynomials

To multiply polynomials, you need to follow these general steps:

1. Multiply each term of the first polynomial by each term of the second polynomial.
2. Add all the resulting terms together, combining like terms.
3. Simplify the resulting expression by combining any remaining like terms.

Here’s an example:

To multiply (x + 3)(2x – 5), you would follow these steps:

1. Multiply each term of the first polynomial (x + 3) by each term of the second polynomial (2x – 5):

$(x+3)(2x-5)$

$=(\cl purple {x})(\cl blue {2x}) + (\cl purple {x})(\cl blue {-5}) + (\cl purple {3})(\cl blue {2x}) + (\cl purple {3})(\cl blue {-5})$
1. Add all the resulting terms together:
$=2x^{2}-5x+6x-15$
1. Simplify the resulting expression by combining like terms:
$=2x^{2}+x-15$

## Multiplying polynomials examples

Here we present several examples of multiplication of polynomials generated with the help of our multiply polynomials calculator.

### Example 01: multiplying a polynomial by a monomial

$5x^{2}y^{2}((-8x^{3})(y^{2})+9xy^{2}-3x)$
$=(\cl purple {5x^{2}y^{2}})(\cl blue {(-8x^{3})(y^{2})} + \cl blue {9xy^{2}} + \cl blue {-3x})$
$=(\cl purple {5x^{2}y^{2}})(\cl blue {(-8x^{3})(y^{2})}) + (\cl purple {5x^{2}y^{2}})(\cl blue {9xy^{2}}) + (\cl purple {5x^{2}y^{2}})(\cl blue {-3x})$
$=-40x^{5}y^{4}+45x^{3}y^{4}-15x^{3}y^{2}$

### Example 02: product of two binomials

$(x+y^{2})(9xy-8)$
$=(\cl purple {x} + \cl purple {y^{2}})(\cl blue {9xy} + \cl blue {-8})$
$=(\cl purple {x})(\cl blue {9xy}) + (\cl purple {x})(\cl blue {-8}) + (\cl purple {y^{2}})(\cl blue {9xy}) + (\cl purple {y^{2}})(\cl blue {-8})$
$=9x^{2}y-8x+9xy^{3}-8y^{2}$
$=9xy^{3}+9x^{2}y-8y^{2}-8x$

### Example 03: multiply a binomial by a polynomial

$(2x+8m)(m^{2}+3xm-m^{2})$
$=(\cl purple {2x} + \cl purple {8m})(\cl blue {m^{2}} + \cl blue {3xm} + \cl blue {-m^{2}})$
$=(\cl purple {2x})(\cl blue {m^{2}}) + (\cl purple {2x})(\cl blue {3xm}) + (\cl purple {2x})(\cl blue {-m^{2}}) + (\cl purple {8m})(\cl blue {m^{2}}) + (\cl purple {8m})(\cl blue {3xm}) + (\cl purple {8m})(\cl blue {-m^{2}})$
$=2m^{2}x+6mx^{2}-2m^{2}x+8m^{3}+24m^{2}x-8m^{3}$
$=24m^{2}x+6mx^{2}$

### Example 04: multiply 3 polynomials together

$(2x+8y^{2}-5xy)(9x^{2}-2z-x)(3x+9y+x^{2})$
$=(\cl purple {(2x+8y^{2}-5xy)(9x^{2}-2z-x)})(\cl blue {3x} + \cl blue {9y} + \cl blue {x^{2}})$
$=(\cl purple {(2x+8y^{2}-5xy)(9x^{2}-2z-x)})(\cl blue {3x}) + (\cl purple {(2x+8y^{2}-5xy)(9x^{2}-2z-x)})(\cl blue {9y}) + (\cl purple {(2x+8y^{2}-5xy)(9x^{2}-2z-x)})(\cl blue {x^{2}})$
$=-135x^{4}y+216x^{3}y^{2}+54x^{4}+15x^{3}y-24x^{2}y^{2}+30x^{2}yz-48xy^{2}z-6x^{3}-12x^{2}z-405x^{3}y^{2}+648x^{2}y^{3}+162x^{3}y+45x^{2}y^{2}-72xy^{3}+90xy^{2}z-144y^{3}z-18x^{2}y-36xyz-45x^{5}y+72x^{4}y^{2}+18x^{5}+5x^{4}y-8x^{3}y^{2}+10x^{3}yz-16x^{2}y^{2}z-2x^{4}-4x^{3}z$
$=-45x^{5}y+72x^{4}y^{2}+18x^{5}-130x^{4}y-197x^{3}y^{2}+10x^{3}yz+648x^{2}y^{3}-16x^{2}y^{2}z+52x^{4}+177x^{3}y-4x^{3}z+21x^{2}y^{2}+30x^{2}yz-72xy^{3}+42xy^{2}z-144y^{3}z-6x^{3}-18x^{2}y-12x^{2}z-36xyz$

## Using the Multiplying Polynomials Calculator in the Classroom

Next, we will explore how to use the calculator in the classroom and the benefits of doing so.

Firstly, using the Multiply polynomials calculator in the classroom can help students understand polynomial multiplication better. Students can use the calculator to check their work or learn how to solve more complex problems.

Another benefit of using the calculator in the classroom is that it can save time. Polynomial multiplication can be a tedious process, especially when dealing with more complex expressions. By using the calculator, students can quickly obtain accurate results and focus on understanding the concepts behind the calculation.

Students who struggle with polynomial multiplication can use the calculator to practice and gain confidence, while more advanced students can use it to tackle more complex problems.