Sure, let's simplify each of the given expressions step by step.
### Simplifying [tex]\((6y^2 + 4y + 5) - (3 - 7y + y^2)\)[/tex]
1. Distribute the negative sign to each term in the second parentheses:
[tex]\[
6y^2 + 4y + 5 - 3 + 7y - y^2
\][/tex]
2. Combine like terms:
- Combine the [tex]\(y^2\)[/tex] terms:
[tex]\[
6y^2 - y^2 = 5y^2
\][/tex]
- Combine the [tex]\(y\)[/tex] terms:
[tex]\[
4y + 7y = 11y
\][/tex]
- Combine the constant terms:
[tex]\[
5 - 3 = 2
\][/tex]
3. Write the simplified expression:
[tex]\[
5y^2 + 11y + 2
\][/tex]
So, the simplified expression is:
[tex]\[
\boxed{5y^2 + 11y + 2}
\][/tex]
### Simplifying [tex]\((x-7)(x+3)\)[/tex]
1. Apply the distributive property (FOIL method):
- First, [tex]\(x \cdot x = x^2\)[/tex]
- Outer, [tex]\(x \cdot 3 = 3x\)[/tex]
- Inner, [tex]\(-7 \cdot x = -7x\)[/tex]
- Last, [tex]\(-7 \cdot 3 = -21\)[/tex]
2. Combine like terms:
[tex]\[
x^2 + 3x - 7x - 21
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
3x - 7x = -4x
\][/tex]
3. Write the simplified expression:
[tex]\[
x^2 - 4x - 21
\][/tex]
So, the simplified expression is:
[tex]\[
\boxed{x^2 - 4x - 21}
\][/tex]
