Distributive property of multiplication over addition and ... - Free Printable

Let's solve each problem using the distributive property, which states:

> $ a \times b + a \times c = a \times (b + c) $

or more generally:

> $ a \times (b + c) = a \times b + a \times c $

We'll simplify each expression step by step.

---

1. $ 44 \times 8 + 44 \times 92 $

Both terms have a common factor of 44.

$$
= 44 \times (8 + 92) = 44 \times 100 = \boxed{4400}
$$

---

2. $ 4 \times 3 \times 12 \times 966 + 144 \times 34 $

First, simplify the first part:
$ 4 \times 3 = 12 $, then $ 12 \times 12 = 144 $, so:

$$
= 144 \times 966 + 144 \times 34
$$

Now both terms have 144 in common.

$$
= 144 \times (966 + 34) = 144 \times 1000 = \boxed{144000}
$$

---

3. $ 127834 \times 1001 - 127834 $

Factor out $ 127834 $:

$$
= 127834 \times (1001 - 1) = 127834 \times 1000 = \boxed{127834000}
$$

---

4. $ 9999 \times 7 + 3 \times 9999 $

Both terms have 9999 as a common factor.

$$
= 9999 \times (7 + 3) = 9999 \times 10 = \boxed{99990}
$$

---

5. $ 16 \times 16 + 2 \times 8 \times 4 $

Simplify second term: $ 2 \times 8 = 16 $, $ 16 \times 4 = 64 $

So:
$$
= 16 \times 16 + 64 = 256 + 64 = \boxed{320}
$$

Alternatively, notice that $ 2 \times 8 \times 4 = 2 \times (8 \times 4) = 2 \times 32 = 64 $ — same result.

But is there a distributive way?

Let’s see: $ 16 \times 16 = 256 $, and $ 2 \times 8 \times 4 = 64 $. No obvious common factor, so just compute directly.

$$
\boxed{320}
$$

---

6. $ 3 \times 15 \times 6 + 4 \times 45 $

First, simplify $ 3 \times 15 = 45 $, then $ 45 \times 6 = 270 $

Second term: $ 4 \times 45 = 180 $

So:
$$
= 270 + 180 = \boxed{450}
$$

Alternatively, note that both terms involve 45:

- $ 3 \times 15 \times 6 = (3 \times 6) \times 15 = 18 \times 15 = 270 $
- But better: $ 3 \times 15 \times 6 = 15 \times (3 \times 6) = 15 \times 18 = 270 $
- And $ 4 \times 45 = 4 \times 45 $

Wait: $ 15 \times 18 = 270 $, $ 4 \times 45 = 180 $

But notice: $ 270 = 6 \times 45 $, $ 180 = 4 \times 45 $

So:
$$
= 6 \times 45 + 4 \times 45 = (6 + 4) \times 45 = 10 \times 45 = \boxed{450}
$$

Nice! Used distributive property.

---

7. $ 49 \times 1444 - 444 \times 7 \times 7 $

Note: $ 49 = 7 \times 7 $, so rewrite:

$$
= (7 \times 7) \times 1444 - 444 \times 7 \times 7
$$

Now both terms have $ 7 \times 7 = 49 $ in common.

Factor out $ 49 $:

$$
= 49 \times (1444 - 444) = 49 \times 1000 = \boxed{49000}
$$

---

8. $ 2 \times 78361 - 836198 \times 0 $

Any number times 0 is 0, so:

$$
= 2 \times 78361 - 0 = 2 \times 78361
$$

Now compute:
$$
2 \times 78361 = 156722
$$

So:
$$
\boxed{156722}
$$

---

✔ Final Answers:

1. $ \boxed{4400} $
2. $ \boxed{144000} $
3. $ \boxed{127834000} $
4. $ \boxed{99990} $
5. $ \boxed{320} $
6. $ \boxed{450} $
7. $ \boxed{49000} $
8. $ \boxed{156722} $

All solved using simplification and the distributive property where applicable.