Question 4 of 43beginner💡 UnderstandShort Answer1 mark

When will (a + b)^2 be equal to a2a^{2} + b2b^{2}?

Correct Answer

(a + b)^2 will be equal to a2a^{2} + b2b^{2} when either a = 0 or b = 0 (or both).

Exercise: Think and Reflect | Q: 3 | (Page 4)
For More Understanding

Explanation

Using the identity (a + b)^2 = a2a^{2} + 2ab + b2b^{2} from the textbook, we can see that the difference between (a + b)^2 and a2a^{2} + b2b^{2} is the term 2ab. For (a + b)^2 to equal a2a^{2} + b2b^{2}, this middle term must be zero. Since 2ab = 0 only when a = 0 or b = 0, this is the condition under which both expressions become equal. The textbook hints at this by asking students to 'use the expansion of (a + b)^2 to decide' which term determines the relationship between the two expressions.

Solution Steps

  1. Step 1: Write the identity: (a + b)^2 = a2a^{2} + 2ab + b2b^{2}

  2. Step 2: For (a + b)^2 = a2a^{2} + b2b^{2}, we need a2a^{2} + 2ab + b2b^{2} = a2a^{2} + b2b^{2}

  3. Step 3: Simplify: 2ab = 0

  4. Step 4: Therefore, either a = 0 or b = 0

PreviousNext