How to Multiply Polynomials
Examine the problem., Multiply the constants.The constants refer to the numerical digits in the problem., Multiply the variables., Write your final answer.
Step-by-Step Guide
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Step 1: Examine the problem.
A problem involving two monomials will only involve multiplication.
There will be no subtraction or addition.
A polynomial problem involving two monomials, or two single-term polynomials, will look something like: (ax) * (by); or (ax) * (bx)' Example: 2x * 3y Example: 2x * 3x Note that a and b represent constants or numerical digits, while x and y represent variables. -
Step 2: Multiply the constants.The constants refer to the numerical digits in the problem.
These are multiplied as they usually would be according to the standard times table.
In other words, during this part of the problem, you are multiplying a and b together.
Example: 2x * 3y = (6)(x)(y) Example: 2x * 3x = (6)(x)(x) , The variables refer to the letters in the equation.
When you multiply these variables, different variables will simply be combined together while like variables will become squared.
Note that when you multiply a variable by a like variable, you raise that variable by another power.
In other words, you are multiplying the x and y or x and x together.
Example: 2x * 3y = (6)(x)(y) = 6xy Example: 2x * 3x = (6)(x)(x) = 6x^2 , Due to the simplified nature of this problem, you will not have any like terms that you need to combine.
The result of (ax) * (by) equals abxy.
Similarly, the result of (ax) * (bx) equals abx^2.
Example: 6xy Example: 6x^2 -
Step 3: Multiply the variables.
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Step 4: Write your final answer.
Detailed Guide
A problem involving two monomials will only involve multiplication.
There will be no subtraction or addition.
A polynomial problem involving two monomials, or two single-term polynomials, will look something like: (ax) * (by); or (ax) * (bx)' Example: 2x * 3y Example: 2x * 3x Note that a and b represent constants or numerical digits, while x and y represent variables.
These are multiplied as they usually would be according to the standard times table.
In other words, during this part of the problem, you are multiplying a and b together.
Example: 2x * 3y = (6)(x)(y) Example: 2x * 3x = (6)(x)(x) , The variables refer to the letters in the equation.
When you multiply these variables, different variables will simply be combined together while like variables will become squared.
Note that when you multiply a variable by a like variable, you raise that variable by another power.
In other words, you are multiplying the x and y or x and x together.
Example: 2x * 3y = (6)(x)(y) = 6xy Example: 2x * 3x = (6)(x)(x) = 6x^2 , Due to the simplified nature of this problem, you will not have any like terms that you need to combine.
The result of (ax) * (by) equals abxy.
Similarly, the result of (ax) * (bx) equals abx^2.
Example: 6xy Example: 6x^2
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David Ward
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