Question

Tamara said the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y). Is she correct? Explain. And what is the correct expression.

Answer 1

Tamara is not quite right there. She was on the right track by multiplying the bases by the 7 outside the parentheses. But the “8” base just had a “y” variable attached to it. Tamara put a “xy” variable after she distributed the 7. The correct expression would be 21x+56y.

Answer 2

Yes, Tamara is correct that the Distributive Property was used to write 21x + 56xy as an equivalent expression, 7(3x + 8y).

The Distributive Property states that for any real numbers a, b, and c, we have:

a(b + c) = ab + ac

This property allows us to distribute a factor to each term within a set of parentheses.

In this case, Tamara used the Distributive Property to rewrite the expression 21x + 56xy as an equivalent expression. She did this by taking the factor of 7 and distributing it to each term within the parentheses:

7(3x + 8y) = (73x) + (78y) = 21x + 56xy

Therefore, the correct expression is 7(3x + 8y).

Explanation: