pply the Distributive Property and Combine like Terms to generate an expression equivalent to 2(a+5)+4(2a+3)−10%0D%0A2%0D%0A(%0D%0A%0D%0A+%0D%0A5%0D%0A)%0D%0A+%0D%0A4%0D%0A(%0D%0A2%0D%0A%0D%0A+%0D%0A3%0D%0A)%0D%0A−%0D%0A10%0D%0A (1 point)%0D%0AResponses%0D%0A%0D%0A9a+12%0D%0A9%0D%0A%0D%0A+%0D%0A12%0D%0A9 A plus 12%0D%0A%0D%0A10a+12%0D%0A10%0D%0A%0D%0A+%0D%0A12%0D%0A10 A plus 12%0D%0A%0D%0A12a+10%0D%0A12%0D%0A%0D%0A+%0D%0A10%0D%0A12 A plus 10%0D%0A%0D%0A10a+22%0D%0A10%0D%0A%0D%0A+%0D%0A22%0D%0A10 A plus 22
To apply the Distributive Property, we need to multiply each term inside the parentheses by the number outside the parentheses and combine like terms.
Given expression: 2(a+5)+4(2a+3)−10
Start by distributing the 2 and 4:
2(a+5) = 2a + 10
4(2a+3) = 8a + 12
The expression now becomes:
2a + 10 + 8a + 12 - 10
Combine like terms:
(2a + 8a) + (10 + 12) - 10
Simplify:
10a + 22 - 10
Combine like terms:
10a + 12
So, an equivalent expression would be 10a + 12.