Distributive Property and Expressions 3

Use the Distributive Property to rewrite and evaluate each expression. 1.6 (5+4)

Answer explanation

Using the Distributive Property: 1.6(5+4) = 1.6*5 + 1.6*4. Calculate: 1.6*5 = 8 and 1.6*4 = 6.4. Add them: 8 + 6.4 = 14.4. Thus, 1.6(5+4) = 14.4.

Use the Distributive Property to rewrite and evaluate each expression. 2.3(2x + 5)

Answer explanation

Apply the Distributive Property: 2.3(2x + 5) = 2.3 * 2x + 2.3 * 5 = 4.6x + 11.5. Thus, the expression simplifies to 4.6x + 11.5.

Use the Distributive Property to rewrite and evaluate each expression. 3. 4(3a 2) + 2(5 – a)

Answer explanation

Apply the Distributive Property: 4(3a^2) + 2(5 - a) = 12a^2 + 10 - 2a. Combine like terms: 12a^2 - 2a + 10. This is the simplified expression.

Use the Distributive Property to rewrite and evaluate each expression. 4.7(4-26)

Answer explanation

Use the Distributive Property: 4.7(4-26) = 4.7*4 - 4.7*26. Calculate: 4.7*4 = 18.8 and 4.7*26 = 122.2. Thus, 18.8 - 122.2 = -103.4.

Use the Distributive Property to rewrite and evaluate each expression. 5.8(2 + 3y) - 4y

Answer explanation

Apply the Distributive Property: 5.8(2) + 5.8(3y) - 4y = 11.6 + 17.4y - 4y = 11.6 + 13.4y. The expression simplifies to 11.6 + 13.4y.

Use the Distributive Property to rewrite and evaluate each expression. 6.5(x + 2) - 3(2x - 4)

Answer explanation

Apply the Distributive Property: 6.5x + 13 - 6x + 12. Combine like terms: (6.5x - 6x) + (13 + 12) = 0.5x + 25. Thus, the expression simplifies to 0.5x + 25.

Use the Distributive Property to rewrite and evaluate each expression. 7.9(3 + 2x)

Answer explanation

Use the Distributive Property: 7.9(3 + 2x) = 7.9*3 + 7.9*2x = 23.7 + 15.8x. Thus, the expression is rewritten as 23.7 + 15.8x.

Use the Distributive Property to rewrite and evaluate each expression. 8. 10(45) + 3(2+3)

Answer explanation

Use the Distributive Property: 10(45) + 3(2+3) = 450 + 3(5) = 450 + 15 = 465. The expression evaluates to 465.

Use the Distributive Property to rewrite and evaluate each expression. 9.2(5x + 3y)

Answer explanation

Apply the Distributive Property: 9.2(5x + 3y) = 9.2 * 5x + 9.2 * 3y = 46x + 27.6y. This rewrites the expression, allowing for easier evaluation or further manipulation.

Use the Distributive Property to rewrite and evaluate each expression. 10. 7(a − 3) + 2(3a + 4)

Answer explanation

Apply the Distributive Property: 7(a - 3) = 7a - 21 and 2(3a + 4) = 6a + 8. Combine: 7a - 21 + 6a + 8 = 13a - 13. Thus, the expression simplifies to 13a - 13.