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Thread: determine the product in 2-3 steps?

  1. #1
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    determine the product in 2-3 steps?

    (3𝑥 − (𝑦 + 1)/3 ) [9x − 𝑥(𝑦 + 1) + (𝑦 + 1) /9 ][9x+ 𝑥(𝑦 + 1) + (𝑦 + 1)/ 9 ] (3𝑥 + (𝑦 + 1)/3
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  2. #2
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    Re: determine the product in 2-3 steps?

    (3𝑥 − (𝑦 + 1)/3 ) [9x − 𝑥(𝑦 + 1) + (𝑦 + 1) /9 ][9x+ 𝑥(𝑦 + 1) + (𝑦 + 1)/ 9 ] (3𝑥 + (𝑦 + 1)/3
    note the pattern where $a = 3x$ and $b = \dfrac{y+1}{3}$

    $(a-b)(a^2-ab+b^2)(a^2+ab+b^2)(a+b)$

    $\left[(a-b)(a^2+ab+b^2)\right] \cdot \left[(a^2-ab+b^2)(a+b)\right]$

    $(a^3-b^3)(a^3+b^3) = a^6 - b^6$
    Thanks from topsquark
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