Printable math worksheet for practicing binomial multiplication using the FOIL method.

Let's solve each of these binomial multiplication problems using the FOIL method.

🔷 FOIL Method Reminder:

FOIL stands for:

- First: Multiply the first terms in each binomial
- Outside: Multiply the outer terms
- Inside: Multiply the inner terms
- Last: Multiply the last terms in each binomial

Then, combine like terms.

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Let’s go through each problem one by one.

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1) $(-a^3 - 5)(-4a^2 - 2)$

Apply FOIL:

- F: $(-a^3)(-4a^2) = 4a^5$
- O: $(-a^3)(-2) = 2a^3$
- I: $(-5)(-4a^2) = 20a^2$
- L: $(-5)(-2) = 10$

Now add all together:

$$
4a^5 + 2a^3 + 20a^2 + 10
$$

✔ Answer: $ \boxed{4a^5 + 2a^3 + 20a^2 + 10} $

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2) $(7p - 3q)(3p - 8q)$

- F: $7p \cdot 3p = 21p^2$
- O: $7p \cdot (-8q) = -56pq$
- I: $-3q \cdot 3p = -9pq$
- L: $-3q \cdot (-8q) = 24q^2$

Add:

$$
21p^2 - 56pq - 9pq + 24q^2 = 21p^2 - 65pq + 24q^2
$$

✔ Answer: $ \boxed{21p^2 - 65pq + 24q^2} $

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3) $(tu + u^2)(-u^2 + 3t)$

Rewrite to make it clearer: $(u^2 + tu)(-u^2 + 3t)$ — order doesn’t matter.

- F: $u^2 \cdot (-u^2) = -u^4$
- O: $u^2 \cdot 3t = 3tu^2$
- I: $tu \cdot (-u^2) = -tu^3$
- L: $tu \cdot 3t = 3t^2u$

Now combine:

$$
-u^4 + 3tu^2 - tu^3 + 3t^2u
$$

We can rearrange in descending powers of $u$:

$$
-u^4 - tu^3 + 3tu^2 + 3t^2u
$$

✔ Answer: $ \boxed{-u^4 - tu^3 + 3tu^2 + 3t^2u} $

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4) $(-8x + 2)(11x + 1)$

- F: $-8x \cdot 11x = -88x^2$
- O: $-8x \cdot 1 = -8x$
- I: $2 \cdot 11x = 22x$
- L: $2 \cdot 1 = 2$

Add:

$$
-88x^2 - 8x + 22x + 2 = -88x^2 + 14x + 2
$$

✔ Answer: $ \boxed{-88x^2 + 14x + 2} $

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5) $(12g - 7)(12g + 7)$

This is a difference of squares pattern!

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

Here, $a = 12g$, $b = 7$

So:

$$
(12g)^2 - (7)^2 = 144g^2 - 49
$$

✔ Answer: $ \boxed{144g^2 - 49} $

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6) $(-9n - 3m)(-6n + 2m)$

- F: $-9n \cdot -6n = 54n^2$
- O: $-9n \cdot 2m = -18nm$
- I: $-3m \cdot -6n = 18mn$
- L: $-3m \cdot 2m = -6m^2$

Now add:

$$
54n^2 - 18nm + 18mn - 6m^2
$$

Note: $-18nm + 18mn = 0$ (since $nm = mn$)

So:

$$
54n^2 - 6m^2
$$

✔ Answer: $ \boxed{54n^2 - 6m^2} $

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7) $(-18b^2 + 6)(1 - 2c^2)$

Treat this as two binomials.

- F: $-18b^2 \cdot 1 = -18b^2$
- O: $-18b^2 \cdot (-2c^2) = 36b^2c^2$
- I: $6 \cdot 1 = 6$
- L: $6 \cdot (-2c^2) = -12c^2$

Now add:

$$
-18b^2 + 36b^2c^2 + 6 - 12c^2
$$

Rearranged:

$$
36b^2c^2 - 18b^2 - 12c^2 + 6
$$

✔ Answer: $ \boxed{36b^2c^2 - 18b^2 - 12c^2 + 6} $

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8) $(5k^2 + 15k^3)(-6k^2 - 2k^4)$

First, note that the order of terms doesn't matter. Let's rewrite both:

$$
(15k^3 + 5k^2)(-2k^4 - 6k^2)
$$

But let's use original order and apply FOIL:

- F: $5k^2 \cdot (-6k^2) = -30k^4$
- O: $5k^2 \cdot (-2k^4) = -10k^6$
- I: $15k^3 \cdot (-6k^2) = -90k^5$
- L: $15k^3 \cdot (-2k^4) = -30k^7$

Now add:

$$
-30k^4 - 10k^6 - 90k^5 - 30k^7
$$

Now arrange in descending powers:

$$
-30k^7 - 10k^6 - 90k^5 - 30k^4
$$

✔ Answer: $ \boxed{-30k^7 - 10k^6 - 90k^5 - 30k^4} $

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✔ Final Answers Summary:

1. $4a^5 + 2a^3 + 20a^2 + 10$
2. $21p^2 - 65pq + 24q^2$
3. $-u^4 - tu^3 + 3tu^2 + 3t^2u$
4. $-88x^2 + 14x + 2$
5. $144g^2 - 49$
6. $54n^2 - 6m^2$
7. $36b^2c^2 - 18b^2 - 12c^2 + 6$
8. $-30k^7 - 10k^6 - 90k^5 - 30k^4$

Let me know if you'd like a step-by-step explanation for any specific problem!