Which of the following is equivalent to (a + b/2)^2 ?

The correct answer is D. Choice D is correct. The expression (a + b/2)^2 can be rewritten as (a + b/2) × (a + b/2) . Using the distributive property, the expression yields (a + b/2) × (a + b/2) = a^2 + (ab)/2 + (ab)/2 + (b^2)/4 . Combining like terms gives a^2 + ab + (b^2)/4 .

Note: The listed a and b values make the original expression and choice D print the same outputs.

SAT Question ad038c19: Answer, Explanation & Desmos Solution

Which of the following is equivalent to $(a + \frac{b}{2})^{2}$ ?

Difficulty:Hard

$a^{2} + \frac{b ^{2}}{2}$

$a^{2} + \frac{b ^{2}}{4}$

$a^{2} + \frac{ab}{2} + \frac{b ^{2}}{2}$

$a^{2} + ab + \frac{b ^{2}}{4}$

Explanation

Enter in Desmos:

Why the other choices are wrong

Student discussion

SAT Question ad038c19: Equivalent Expressions answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong

Student discussion