Express 100 as the difference of two squares.

Question 6 of 27intermediate🔧 ApplyShort Answer2 marks

Correct Answer

Identity: $a^2 - b^2 = (a + b)(a - b)$

Given: $(a + b)(a - b) = 100$

Factor pairs of 100: $(10, 10)$ , $(20, 5)$ , $(50, 2)$ , $(100, 1)$ , $(25, 4)$

Solution 1: If $a + b = 20$ and $a - b = 5$ : $a = 12.5$ , $b = 7.5$ ∴ $12.5^2 - 7.5^2 = 100$

Solution 2: If $a + b = 50$ and $a - b = 2$ : $a = 26$ , $b = 24$ ∴ $26^2 - 24^2 = 100$

Solution 3: If $a + b = 25$ and $a - b = 4$ : $a = 14.5$ , $b = 10.5$ ∴ $14.5^2 - 10.5^2 = 100$

Exercise: Figure it Out (Section 2) | Q: 2 | (Page Page 14)

For More Understanding

Explanation

The chapter presents Identity 1C: $(a + b)(a - b) = a^2 - b^2$ . To express 100 as a difference of squares, we find factor pairs of 100 and solve for $a$ and $b$ .

Solution Steps

Use identity: $a^2 - b^2 = (a + b)(a - b) = 100$
Find factor pairs of 100: (20, 5), (50, 2), (25, 4), etc.
For (50, 2): $a + b = 50$ , $a - b = 2$ → $a = 26$ , $b = 24$
Verify: $26^2 - 24^2 = 676 - 576 = 100$

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