If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

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Question: If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

Options:

Correct Answer: 4

Solution:

(a + b)² = (2 + 3)² = 25; a² + b² = 2² + 3² = 4 + 9 = 13; thus, 25 - 13 = 12.

If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

If a = 2 and b = 3, what is the value of (a + b)² - (a² + b²)?

Step 1: Identify the values of a and b. Here, a = 2 and b = 3.
Step 2: Calculate (a + b). This means add a and b together: 2 + 3 = 5.
Step 3: Square the result from Step 2. This means multiply 5 by itself: 5 * 5 = 25.
Step 4: Calculate a². This means multiply a by itself: 2 * 2 = 4.
Step 5: Calculate b². This means multiply b by itself: 3 * 3 = 9.
Step 6: Add the results from Step 4 and Step 5 together: 4 + 9 = 13.
Step 7: Subtract the result from Step 6 from the result in Step 3: 25 - 13 = 12.

Algebraic Expansion – Understanding how to expand and simplify expressions involving squares and sums.
Difference of Squares – Recognizing the relationship between (a + b)² and a² + b².