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Factor each expression

(X+5)^3-(2x+1)^3

  • math - ,

    Using A^3 - b^3 = (A+B)(A^2 + AB + B^2)

    (x+5)^3-(2x+1)^3
    =( x+5 - 2x-1)( (x+5)^2 + (x+5)(2x+1) + (2x+1)^2 )
    = (4-x)(x^2 + 10x + 25 + 2x^2 + 11x + 5 + 4x^2 + 4x + 1)
    = (4-x)(7x^2 + 25x + 31)

    Here is a neat way to check our answer,
    let x be any value, say x = 1

    original value = 6^3 - 3^3 = 189
    factored form value = 3(63) = 189
    Even though this does not "prove" that my answer is correct, there is an extremely high probability that my answer is correct.

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