Question

1. $(11b^4 - 3b^4) - (3b^4 - 11b^4 + 7b)$
2. $(12p + 14p^5) + (8 - 14p^5 - 4p)$
3. $(14p^3 + 4p^4) - (4p^4 - 14p^3 + 14p^5)$
4. $(12b + 4b^7) - (5b^7 + 4b^3 - 11b)$
5. $(-5m^3 + 12m^5 + 9m^2) + (5m^2 + 6m^5 - 9m^3)$
6. $(-12k - 6k^2 - 12k^4) + (-5k - 6k^2 - 11k^4)$
7. $(11r^4 - 8 - 4r^3) - (10r^2 - 2 - 14r^4)$
8. $(-6p^2 - 12 + 13p^3) + (-3p^3 - 11p^3 - 2)$
9. $(-4 - 11n^2 - 4n^4) - (-2 + 3n^2 - 9n^4)$

find each product. use distribution!

1. $4(3p + 5)$
2. $4n(n + 4)$
3. $5(2x + 3)$
4. $3(2n - 3)$
5. $4(4b - 3)$
6. $4(x - 1)$
7. $2r^2(5r + 4)$
8. $4(2a + 1)$
9. $2x^2(2x - 3)$
10. $2n^2(2n - 2)$
11. $(-x + 3)(-3x + 2)$
12. $(6x - 8)(-2x + 5)$
13. $(7x + 7)(-5x + 7)$
14. $(-3n + 3)(-5n - 8)$
15. $(-3n + 6)(-5n + 2)$
16. $(4x - 8)(-5x + 2)$
17. $(3n - 1)(-4n + 2)$
18. $(3n - 1)(7n + 5)$

Explanation:

Let's solve problem 40: \( 4(3p + 5) \) using the distributive property (also known as the distributive law of multiplication over addition).

Step 1: Apply the distributive property

The distributive property states that \( a(b + c) = ab + ac \). Here, \( a = 4 \), \( b = 3p \), and \( c = 5 \). So we distribute the 4 to both terms inside the parentheses.
\[
4(3p + 5) = 4 \times 3p + 4 \times 5
\]

Step 2: Simplify each term

Calculate \( 4 \times 3p \) and \( 4 \times 5 \).
\[
4 \times 3p = 12p
\]
\[
4 \times 5 = 20
\]

Step 3: Combine the simplified terms

Put the two simplified terms together.
\[
12p + 20
\]

Answer:

\( 12p + 20 \)