Question

Select Equivalent or Not equivalent for each pair of expressions.

Equivalent
Not equivalent
3(a−b) and 3a−3b
2a(2+b) and 4ab

Answer 1

The first pair of expressions 3(a−b) and 3a−3b are equivalent by distribution, while the second pair 2a(2+b) and 4ab are not equivalent as the former has an additional term when expanded.

Step-by-step explanation:

The question involves determining whether pairs of algebraic expressions are equivalent. Equivalence in this context means that the expressions will yield the same result for any substitution of variables with numbers.

For the first pair, 3(a−b) and 3a−3b, applying the distributive property of multiplication over subtraction shows that they are equivalent because:

3(a−b) = 3*a − 3*b = 3a − 3b

For the second pair, 2a(2+b) and 4ab, expanding the first expression using the distributive law:

2a(2+b) = 2a*2 + 2a*b = 4a + 2ab

This is not equivalent to 4ab because there is an additional term, 4a, which is not present in 4ab. Therefore, 2a(2+b) and 4ab are not equivalent.