# Lesson 24

Polynomial Identities (Part 2)

- Let’s explore some other identities.

### Problem 1

Is \(a^6 + b^6 = (a^2+b^2)(a^4 - a^2b^2 + b^4)\) an identity? Explain or show your reasoning.

### Problem 2

Match each lettered expression with the number of an expression equivalent to it.

### Problem 3

Let \((x^2+5x+4)(x+2)=A(x+1)\). If this is an identity, what is a possible expression for \(A\)?

### Problem 4

What are the points of intersection between the graphs of the functions \(f(x)=(x + 6)(2x+1)\) and \(g(x)=2x+1\)?

### Problem 5

Identify all values of \(x\) that make the equation true.

- \(\frac{x+5}{x+11}=\frac{1}{x+5}\)
- \(\frac{2x-3}{x} = \frac{14}{x+5}\)

### Problem 6

Match each expression in the lettered list with the number of an expression equivalent to it.