Choose the expression that has the same value as the following:
(x−7)2
To solve the problem, we need to expand the expression (x−7)2 using the formula for the square of a difference.
The formula for the square of a difference is (a−b)2=a2−2ab+b2.
Let's apply this formula to our expression (x−7)2:
- Identify a=x and b=7.
- Substitute these values into the formula: (x−7)2=x2−2(x)(7)+72.
- Calculate each term:
- x2 remains as x2.
- −2(x)(7)=−14x.
- 72=49.
So, expanding the expression, we get x2−14x+49.
Thus, the expression that has the same value as (x−7)2 is x2−14x+49.
x2−14x+49