Question 5 of 27beginner💡 UnderstandShort Answer2 marks

Which is greater: (a−b)2(a - b)^2 or (b−a)2(b - a)^2? Justify your answer.

Correct Answer

(a−b)2(a - b)^2 and (b−a)2(b - a)^2 are equal.

Justification:

(b−a)2=(−(a−b))2(b - a)^2 = (-(a - b))^2 =(−1)2(a−b)2= (-1)^2(a - b)^2 =(a−b)2= (a - b)^2

Reason: When we square any number, whether positive or negative, the result is always positive. Since (a−b)(a - b) and (b−a)(b - a) are negatives of each other, their squares are equal.

Exercise: Figure it Out (Section 2) | Q: 1 | (Page Page 14)
For More Understanding

Explanation

The chapter discusses the identity (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2. Note that (b−a)2=b2−2ba+a2=a2−2ab+b2=(a−b)2(b - a)^2 = b^2 - 2ba + a^2 = a^2 - 2ab + b^2 = (a - b)^2. Both expressions expand to the same result.

Solution Steps

  1. Expand (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2

  2. Expand (b−a)2=b2−2ba+a2=a2−2ab+b2(b - a)^2 = b^2 - 2ba + a^2 = a^2 - 2ab + b^2

  3. Both expressions are identical, so they are equal

PreviousNext