Edia | Free math homework in minutes - Free Printable

Let's solve each problem step by step. These are special cases of binomial multiplication, specifically squaring a binomial.

The formula for squaring a binomial is:

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

or

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

We can also use the distributive property (FOIL) to expand:
(First, Outer, Inner, Last)

But since these are squares, we'll use the pattern:

$$
(A + B)^2 = A^2 + 2AB + B^2
$$

Let’s go through each one.

---

1. $(-3k - 4)^2$

This is of the form $(a + b)^2$, where $a = -3k$, $b = -4$

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

$$
= 9k^2 + 24k + 16
$$

✔ Answer: $9k^2 + 24k + 16$

---

2. $(-2y - 1)^2$

$a = -2y$, $b = -1$

$$
(-2y - 1)^2 = (-2y)^2 + 2(-2y)(-1) + (-1)^2
$$

$$
= 4y^2 + 4y + 1
$$

✔ Answer: $4y^2 + 4y + 1$

---

3. $(-3a - 5)^2$

$a = -3a$, $b = -5$

$$
(-3a - 5)^2 = (-3a)^2 + 2(-3a)(-5) + (-5)^2
$$

$$
= 9a^2 + 30a + 25
$$

✔ Answer: $9a^2 + 30a + 25$

---

4. $(n + 3)^2$

$a = n$, $b = 3$

$$
(n + 3)^2 = n^2 + 2(n)(3) + 3^2 = n^2 + 6n + 9
$$

✔ Answer: $n^2 + 6n + 9$

---

5. $(-2c + 1)^2$

This is $(-2c + 1)^2$, so $a = -2c$, $b = 1$

$$
(-2c + 1)^2 = (-2c)^2 + 2(-2c)(1) + (1)^2
$$

$$
= 4c^2 - 4c + 1
$$

✔ Answer: $4c^2 - 4c + 1$

---

6. $(-c + 2)^2$

$a = -c$, $b = 2$

$$
(-c + 2)^2 = (-c)^2 + 2(-c)(2) + (2)^2
$$

$$
= c^2 - 4c + 4
$$

✔ Answer: $c^2 - 4c + 4$

---

7. $(-c + 1)^2$

$a = -c$, $b = 1$

$$
(-c + 1)^2 = (-c)^2 + 2(-c)(1) + (1)^2
$$

$$
= c^2 - 2c + 1
$$

✔ Answer: $c^2 - 2c + 1$

---

8. $(2b - 5)^2$

$a = 2b$, $b = -5$

$$
(2b - 5)^2 = (2b)^2 + 2(2b)(-5) + (-5)^2
$$

$$
= 4b^2 - 20b + 25
$$

✔ Answer: $4b^2 - 20b + 25$

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1. $(-3k - 4)^2$ | $9k^2 + 24k + 16$ |
| 2. $(-2y - 1)^2$ | $4y^2 + 4y + 1$ |
| 3. $(-3a - 5)^2$ | $9a^2 + 30a + 25$ |
| 4. $(n + 3)^2$ | $n^2 + 6n + 9$ |
| 5. $(-2c + 1)^2$ | $4c^2 - 4c + 1$ |
| 6. $(-c + 2)^2$ | $c^2 - 4c + 4$ |
| 7. $(-c + 1)^2$ | $c^2 - 2c + 1$ |
| 8. $(2b - 5)^2$ | $4b^2 - 20b + 25$ |

---

🔍 Key Concept:

When squaring a binomial $(A + B)^2$, always remember:
- Square the first term
- Twice the product of both terms
- Square the last term

And pay attention to signs, especially when negative numbers are involved.

Let me know if you'd like this in a printable format or with more explanation!