Find Equivalent Expressions for (x-7)²: Perfect Square Expansion

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 $(a-b)^2 = a^2 - 2ab + b^2$.

Let's apply this formula to our expression $(x-7)^2$:

• Identify $a = x$ and $b = 7$.
• Substitute these values into the formula: $(x-7)^2 = x^2 - 2(x)(7) + 7^2$.
• Calculate each term:
• $x^2$ remains as $x^2$.
• $-2(x)(7) = -14x$.
• $7^2 = 49$.

So, expanding the expression, we get $x^2 - 14x + 49$.

Thus, the expression that has the same value as $(x-7)^2$ is $x^2 - 14x + 49$.