Simplify the following expression x15x+20x+5x7x

Mathematics

ScanSolve AI Answer

Answer

50x2+20x50x^2 + 20x

Step-by-step solution

3 steps

The expression given is x15x+20x+5x7xx_{15}x+20x+5x_7x. The notation x15xx_{15}x and x7xx_7x is ambiguous. For the purpose of simplification, I will assume that the numbers in the subscript are coefficients that multiply the variable xx, and then are multiplied by the adjacent xx.
Therefore, x15xx_{15}x is interpreted as 15⋅x⋅x=15x215 \cdot x \cdot x = 15x^2.
And 5x7x5x_7x is interpreted as 5⋅7⋅x⋅x=35x25 \cdot 7 \cdot x \cdot x = 35x^2.

  1. Rewrite the expression using the assumed interpretation.

    x15x+20x+5x7x=15x2+20x+35x2x_{15}x+20x+5x_7x = 15x^2 + 20x + 35x^2
  2. Identify and group like terms.

    The terms 15x215x^2 and 35x235x^2 are like terms because they both contain x2x^2.

    (15x2+35x2)+20x(15x^2 + 35x^2) + 20x
  3. Combine the like terms.

    Add the coefficients of the x2x^2 terms:

    (15+35)x2+20x=50x2+20x(15+35)x^2 + 20x = 50x^2 + 20x

    The simplified expression is:

    50x2+20x50x^2 + 20x
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