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How Do You Multiply Trinomials?

Find the product of the two polynomials 2x2+3x+4 and 2x2+2x+6

Summary

  1. 'x' is a variable
  2. Multiply the first trinomial by the second trinomial by distributing the terms
  3. Multiplying the first term, 2x2, through the second trinomial gives us 2x4, 4x3, and 12x2
  4. Multiplying the second term, 3x, through the second trinomial gives us 3x3, 6x2, and 18x
  5. Multiplying the third term, 4, through the second trinomial gives us 4x2, 8x, and 24

Notes

    1. 'x' is a variable
    1. We're multiplying the first term in the left trinomial by everything in the right trinomial
    1. The first term in the first trinomial is 2x2
    1. Multiply 2x2 by every term in the second trinomial
    2. The second trinomial is x2+2x+6
    1. 'x' is a variable
    2. Multiply the first terms of each trinomial together, 2x2•x2
    3. Multiply the first term of the left trinomial by the second term in the right trinomial, 2x2•2x
    4. Multiply the first term of the left trinomial by the last term in the right trinomial, 2x2•6
    1. 'x' is a variable
    2. 2x2•x2=2x4
    3. 2x2•2x=4x3
    4. 2x2•6=12x2
    1. The second term in the first trinomial is 3x
    2. 'x' is a variable
    1. Multiply 3x by every term in the second trinomial
    2. The second trinomial is x2+2x+6
    3. 'x' is a variable
    1. 'x' is a variable
    2. Multiply the second term in the first trinomial by the first term in the second trinomial, 3x•x2
    3. Multiply the second terms in each trinomial together, 3x•2x
    4. Multiply the first second of the left trinomial by the last term in the right trinomial, 3x•6
    1. 'x' is a variable
    2. 3x•x2=3x3
    3. 3x•2x=6x2
    4. 3x•6=18x
    1. The third term in the first trinomial is 4
    1. Multiply 4 by every term in the second trinomial
    2. The second trinomial is x2+2x+6
    3. 'x' is a variable
    1. 'x' is a variable
    2. Multiply the last term in the left trinomial by the first term in the right trinomial, 4•x2
    3. Multiply the last term of the left trinomial by the second term in the right trinomial, 4•2x
    4. Multiply the last terms in each trinomial together, 4•6
    1. 'x' is a variable
    2. 4•x2=4x2
    3. 4•2x=8x
    4. 4•6=24
    1. Like terms will have an 'x' to the common power
    1. The only term with 'x' to the 4th is the 2x4
    1. These terms have 'x' to the 3rd in common
    1. These terms have 'x' to the 2nd in common
    1. These terms have 'x' to the 1st in common
    1. The only term with 'x' to the 0 power is 24
    1. 4x3+3x3=7x3
    2. 12x2+6x2+4x2=22x2
    3. 18x+8x=26x