Question
Factor the following expression completely: \( 16 x^{2}-56 x+49=\square \)
Ask by Bowman Montgomery. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(16x^{2}-56x+49 = (4x-7)^{2}\)
Solution
Factor the expression \( 16x^2-56x+49 \).
Factor the expression by following steps:
- step0: Factor:
\(16x^{2}-56x+49\)
- step1: Factor the expression:
\(\left(4x-7\right)^{2}\)
The expression \(16x^{2}-56x+49\) can be factored completely as \((4x-7)^{2}\).
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Simplify this solution Bonus Knowledge
To factor the expression \(16x^2 - 56x + 49\), let's start by recognizing that it can be rearranged using the perfect square form. Notice that: 1. The expression is structured as \(Ax^2 - Bx + C\). 2. Here, \(A = 16\), \(B = 56\), and \(C = 49\). We see that \(16\) is \(4^2\), \(49\) is \(7^2\), and we can check to see if the middle term can align with a perfect square trinomial: \[ (4x - 7)^2 = 16x^2 - 2(4x)(7) + 49 = 16x^2 - 56x + 49 \] Thus, \(16x^2 - 56x + 49\) can be completely factored as: \[ (4x - 7)^2 \] So the answer is: \[ (4x - 7)^2 \]
