The problem shown in the image is to simplify the expression $(-4x + 3)^2$. Let's solve it step by step.

Step-by-step solution:

We are squaring the binomial $(-4x + 3)$. The formula for squaring a binomial is:

$(a + b)^2 = a^2 + 2ab + b^2$

Here:

• $a = -4x$
• $b = 3$

Substitute into the formula:

$(-4x + 3)^2 = (-4x)^2 + 2(-4x)(3) + 3^2$

1. Calculate $(-4x)^2$: $(-4x)^2 = 16x^2$

2. Calculate $2(-4x)(3)$: $2(-4x)(3) = -24x$

3. Calculate $3^2$: $3^2 = 9$

Combine all the terms:

$(-4x + 3)^2 = 16x^2 - 24x + 9$

Final Answer:

$16x^2 - 24x + 9$

Let me know if you would like further clarifications or details! 😊

Here are 5 related questions you could explore:

1. How would the solution change if the expression were $(-4x - 3)^2$?
2. What is the general formula for $(a + b)^n$ when $n = 2$?
3. How would this problem differ if you had to simplify $(-4x + 3)^3$?
4. Can you graph the function $y = 16x^2 - 24x + 9$? What is its vertex?
5. How does this problem relate to factoring perfect square trinomials?

Tip: Always apply the binomial expansion formula carefully when squaring expressions—it helps avoid errors!