Question 499455
This is a very tedious problem, with lots of potential for mistakes.
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{{{ ((1/4)x^2-2/7)(-(1/2)x-1/2) }}}
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Let:
{{{ s = (1/4)*x^2 }}}
{{{ t = 2/7 }}}
{{{ u = -(1/2)*x }}}
{{{ v = 1/2 }}}
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Substitute
{{{ (s-t)(u-v) }}}
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Use FOIL to define terms
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{{{ s*u - s*v - t*u + t*v }}}
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Now substitute for s, t, u & v
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{{{ (1/4)*x^2*(-1/2)*x - (1/4)*x^2*(1/2) - (2/7)*(-1/2)*x + (2/7)*(1/2) }}}
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Rearrange the multiplications since their order does not affect values
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{{{ (1/4)(-1/2)*x^2*x - (1/4)(1/2)x^2 - (2/7)*(-1/2)*x + (2/7)*(1/2) }}}
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Simplify
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{{{-(1/8)*x^3 - (1/8)*x^2 + (2/14)*x + 2/14}}}
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multiply through by 112 to eliminate fractions
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{{{-14x^3 - 14x^2 +16x + 16}}}
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divide through by 2
{{{-7x^3 -7x^2 +8x + 8}}}
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{{{graph(500,500,-3,3,-10,10,-7*x^3 - 7*x^2 +8*x + 8)}}}