Question 58554
Determine whether or not the trinomials are perfect squares:
{{{4x^2-20x+25}}} Divide by the coefficient of the x^2 term (4)
{{{x^2 - 5x + 25/4}}} Now find the square of half the x-coefficient: {{{((-5)/2)^2 = 25/4}}}. Does this equal the constant term of the trinomial {{{25/4}}}?  Yes it does, so the trinomial is a perfect square.
{{{4x^2-20x+25 = (2x-5)(2x-5)}}} = {{{(2x-5)^2}}}
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{{{64u^2+72uv+81v^2}}} Divide by 64.
{{{u^2+(9/8)uv + (81/64)v^2}}} Find the square of half the x-coefficient: {{{(9/16)^2 = 81/256}}} not = to {{{81/64}}} therefore, the trinomial is not a perfect square.