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How Do You Solve a Word Problem by Multiplying Trinomials?

Dominic is stitching together a quilt from a number of rectangular pieces. He made the diagram that you see for the final size of the quilt. When it is all stitched together what will be the total area of the quilt be? Write the answer as a polynomial in simplest form.

Summary

  1. 'x' is a variable
  2. Write an equation for the horizontal side, 2x2+3x+4
  3. Write an equation for the vertical side, x2+2x+6
  4. Multiply the adjacent sides together to find the area of the quilt
  5. Identify and then combine like terms together

Notes

    1. We are looking at the horizontal side first, the side with 2x2, 3x, and 4
    2. 'x' is a variable
    1. We're adding together the horizontal lengths
    2. 2x2+3x+4
    3. 'x' is a variable
    1. We are looking at the vertical side second, the side with x2, 2x, and 6
    2. 'x' is a variable
    1. We're adding together the vertical lengths
    2. x2+2x+6
    3. 'x' is a variable
    1. 'x' is a variable
    2. The horizontal side is 2x2+3x+4
    3. The vertical side is x2+2x+6
    1. Remember, the area of a rectangle is just the product of two adjacent sides
    1. Each equation is a polynomial
    1. We're going to multiply the first term of the left equation by everything in the right equation
    1. The 2nd polynomial is x2+2x+6
    2. 'x' is a variable
    1. 'x' is a variable
    2. 2x2 times x2 equals 2x4
    3. 2x2 times 2x equals 4x3
    4. 2x2 times 6 equals 12x2
    1. We're going to multiply the second term of the left equation by everything in the right equation
    1. The 2nd polynomial is x2+2x+6
    2. 'x' is a variable
    1. 'x' is a variable
    2. 3x times x2 equals 3x3
    3. 3x times 2x equals 6x2
    4. 3x times 6 equals 18x
    1. We're going to multiply the third term of the left equation by everything in the right equation
    1. The 2nd polynomial is x2+2x+6
    2. 'x' is a variable
    1. 'x' is a variable
    2. 4 times x2 equals 4x2
    3. 4 times 2x equals 8x
    4. 4 times 6 equals 24
    1. Like terms will have an 'x' raised to the same power
    2. 'x' is a variable
    1. Like terms will have an 'x' raised to the same power
    2. No terms besides 2x4 have a 4th power
    3. 'x' is a variable
    1. Like terms will have an 'x' raised to the same power
    2. These are the terms that have 'x' to the 3rd power
    3. 'x' is a variable
    1. Like terms will have an 'x' raised to the same power
    2. These are the terms that have 'x' to the 2nd power
    3. 'x' is a variable
    1. Like terms will have an 'x' raised to the same power
    2. These are the terms that have 'x' to the 1st power
    3. 'x' is a variable
    1. Like terms will have an 'x' raised to the same power
    2. No terms besides 24 have an 'x' to the 0th power
    3. 'x' is a variable
    1. 'x' is a variable
    2. 3x3+4x3 = 7x3
    3. 12x2+6x2+4x2=22x2
    4. 18x+8x=26x