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Math Help - how do you simplify with expanding?

  1. #1
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    how do you simplify without expanding?

    I am reading an example on mathlab and it is simplifying a derivative using the product rule and the chain rule. I just want to know how the example simplifies without expanding.

    \frac{dy}{dx}=(14(7x-2))(3-x^5)^2+(7x-2)^2(-10x^4(3-x^5))

    = \frac{dy}{dx}=(2(7x-2)(3-x^5)[-5x^4(7x-2)+7(3-x^5)]
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  2. #2
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    Re: how do you simplify without expanding?

    Hello, delgeezee!


    We have: . y \;=\;(7x-2)^2(3-x^5)^2

    Product/Chain Rule: . \frac{dy}{dx} \;=\;2\!\cdot\!(7x-2)\!\cdot\!7\!\cdot\!(3-x^5)^2 + (7x-2)^2\!\cdot\!2(3-x^5)\!\cdot\!(-5x^4)

    Simplify a bit: . . . . . . \frac{dy}{dx} \;=\;14(7x-2)(3-x^5)^2 - 10x^4(7x-2)^2(3-x^5)


    We have two groups: . \frac{dy}{dx} \;=\;\underbrace{14(7x-2)(3-x^5)^2} - \underbrace{10x^4(7x-2)^2(3-x^5)}

    They have common factors: . 2,\;(7x-2),\;\text{and }(3-x^5)

    Factor them out!

    . . \frac{dy}{dx} \;=\;2(7x-2)(3-x^5)\,\bigg[7(3-x^5) - 5x^4(7x-2)\bigg]

    . m . . =\;2(7x-2)(3-x^5)\,\big[21 - 7x^5 - 35x^5 + 10x^4\big]

    . m . . =\;2(7x-2)(3-x^5)(21 + 10x^4 - 42x^5)

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  3. #3
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    Re: how do you simplify without expanding?

    Aha, now that makes sense!
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