Find the product. $$ (x-7)^{2} $$

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UpStudy AI · Accepted Answer

1. Write the expression as a product of two binomials:
   $$
   (x-7)^2 = (x-7)(x-7)
   $$

2. Multiply the two binomials using the distributive property (FOIL method):
   $$
   (x-7)(x-7) = x \cdot x + x \cdot (-7) -7 \cdot x -7 \cdot (-7)
   $$

3. Perform the multiplications:
   $$
   x \cdot x = x^2,\quad x \cdot (-7) = -7x,\quad -7 \cdot x = -7x,\quad -7 \cdot (-7) = 49
   $$

4. Combine like terms:
   $$
   x^2 - 7x - 7x + 49 = x^2 - 14x + 49
   $$

The final expanded product is:
$$
x^2 - 14x + 49
$$
The product of $$ (x-7)^2 $$ is $$ x^2 - 14x + 49 $$.

Find the product. \[ (x-7)^{2} \]

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