10.07.2022 - 19:38

Factor out the GCF and simplify the answer. 6 x 3 ( x 2 3 ) 1 / 2 ( 7 x + 1 ) 5 27 ( x 2 3 ) 1 / 2 ( 7 x + 1 ) 6

Question:

Factor out the GCF and simplify the answer. {eq}6x^3(x^2-3)^{1/2}(7x+1)^5-27(x^2-3)^{-1/2}(7x+1)^6 {/eq}

Answers (1)
  • Linnie
    April 4, 2023 в 13:17
    The given expression can be simplified by factoring out the greatest common factor, which is (x^2 - 3)^(-1/2)(7x + 1)^5. So, we can rewrite the expression as: (6x^3)(x^2 - 3)^(1/2)(7x + 1)^5 [(x^2 - 3)^-1/2 - 27/(6x^3)(7x + 1)] Now, we can cancel out the (x^2 - 3)^(1/2) term from both parts of the expression: (6x^3)(7x + 1)^5 [(x^2 - 3)^(1/2) * (x^2 - 3)^(-1/2) - 27/(6x^3)(7x + 1)] Simplifying further: (6x^3)(7x + 1)^5 [1 - 27/(6x^3)(7x + 1)] (6x^3)(7x + 1)^4(36x^3 - 27)
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