Factor. u^2 - 8u + 16 ______

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form (a - b)^2 = a^2 - 2ab + b^2. We need to check if u^2 - 8u + 16 fits this pattern.Identify Square Roots: Identify the square root of the first term and the last term. The square root of u^2 is u, and the square root of 16 is 4. So, we have a = u and b = 4.Verify Middle Term: Check if the middle term fits the pattern 2ab. For our expression, the middle term is -8u. We need to see if this is equal to 2 * u * 4. 2 * u * 4 = 8u. Since the middle term is -8u, it fits the pattern with a negative sign.Write Factored Form: Write the factored form using the identified values of a and b. Since the middle term is negative, we use (a - b)^2 to factor the expression. (u - 4)^2 is the factored form of u^2 - 8u + 16.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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u^2 - 8u + 16

Check Quadratic Form: Determine if the quadratic can be factored as a perfect square trinomial. A perfect square trinomial is in the form $(a - b)^2 = a^2 - 2ab + b^2$ . We need to check if $u^2 - 8u + 16$ fits this pattern.
Identify Square Roots: Identify the square root of the first term and the last term. $\newline$ The square root of $u^2$ is $u$ , and the square root of $16$ is $4$ . So, we have $a = u$ and $b = 4$ .
Verify Middle Term: Check if the middle term fits the pattern $2ab$ . For our expression, the middle term is $-8u$ . We need to see if this is equal to $2 \times u \times 4$ . $2 \times u \times 4 = 8u$ . Since the middle term is $-8u$ , it fits the pattern with a negative sign.
Write Factored Form: Write the factored form using the identified values of $a$ and $b$ . Since the middle term is negative, we use $(a - b)^2$ to factor the expression. $(u - 4)^2$ is the factored form of $u^2 - 8u + 16$ .