How do you factor a perfect square trinomial $4 a^{2} - 10 a - 25$ $4a^2 − 10a − 25$ ?

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Answer 1 · 2015-06-07T16:39:53

The equation #4a^2-10a-25 is not a perfect square trinomial. You will have to factor it with the quadratic formula.

Perfect square trinomials are the result of squaring binomials:

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $(a+b)^2=a^2+2ab+b^2$
${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$ $(a-b)^2=a^2-2ab+b^2$

The last number in a perfect square trinomial cannot be negative because it is a squared number. For example:

${(3 x - 5)}^{2} = (3 x - 5) (3 x - 5)$ $(3x-5)^2=(3x-5)(3x-5)$

Foil $(3 x - 5) (3 x - 5)$ $(3x-5)(3x-5)$ .

$9 x^{2} - 15 x - 15 x + 25$ $9x^2-15x-15x+25$ =

$9 x^{2} - 30 x + 25$ $9x^2-30x+25$

How do you factor a perfect square trinomial 4a^2 − 10a − 254a2−10a−25 4a^2 − 10a − 25?