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

Question

Choose the expression that has the same value as the following:

(x7)2 (x-7)^2

Video Solution

Solution Steps

00:00 Simply
00:03 We will use the shortened multiplication formulas to expand the brackets
00:15 X is the A in the formula
00:18 And 7 is the B in the formula
00:28 We'll substitute according to the formula and get the expansion of the brackets
00:36 We'll solve the multiplications
00:41 And this is the solution to the question

Step-by-Step Solution

To solve the problem, we need to expand the expression (x7)2(x-7)^2 using the formula for the square of a difference.

The formula for the square of a difference is (ab)2=a22ab+b2(a-b)^2 = a^2 - 2ab + b^2.

Let's apply this formula to our expression (x7)2(x-7)^2:

  • Identify a=xa = x and b=7b = 7.
  • Substitute these values into the formula: (x7)2=x22(x)(7)+72(x-7)^2 = x^2 - 2(x)(7) + 7^2.
  • Calculate each term:
    • x2x^2 remains as x2x^2.
    • 2(x)(7)=14x-2(x)(7) = -14x.
    • 72=497^2 = 49.

So, expanding the expression, we get x214x+49x^2 - 14x + 49.

Thus, the expression that has the same value as (x7)2(x-7)^2 is x214x+49x^2 - 14x + 49.

Answer

x214x+49 x^2-14x+49