Question
Simplify the product.
(x + 5)(x + 7)=
(x + 5)(x + 7)=
Answers
GPT-4o mini
To simplify the product \((x + 5)(x + 7)\), you can use the distributive property (also known as the FOIL method for binomials):
\[
(x + 5)(x + 7) = x(x) + x(7) + 5(x) + 5(7)
\]
Now, performing the multiplication:
1. \(x \cdot x = x^2\)
2. \(x \cdot 7 = 7x\)
3. \(5 \cdot x = 5x\)
4. \(5 \cdot 7 = 35\)
Now, combine all these terms:
\[
x^2 + 7x + 5x + 35
\]
Combine the like terms (\(7x + 5x\)):
\[
x^2 + 12x + 35
\]
So, the simplified product is:
\[
\boxed{x^2 + 12x + 35}
\]
\[
(x + 5)(x + 7) = x(x) + x(7) + 5(x) + 5(7)
\]
Now, performing the multiplication:
1. \(x \cdot x = x^2\)
2. \(x \cdot 7 = 7x\)
3. \(5 \cdot x = 5x\)
4. \(5 \cdot 7 = 35\)
Now, combine all these terms:
\[
x^2 + 7x + 5x + 35
\]
Combine the like terms (\(7x + 5x\)):
\[
x^2 + 12x + 35
\]
So, the simplified product is:
\[
\boxed{x^2 + 12x + 35}
\]