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25^(2)-15^(2)=...

`25^(2)-15^(2)=` ___

A

`(25+15)^(2)`

B

`(25-15)^(2)`

C

`(25+15)(25-15)`

D

`25xx15`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem \( 25^2 - 15^2 \), we can use the algebraic identity for the difference of squares, which states: \[ a^2 - b^2 = (a + b)(a - b) \] ### Step-by-Step Solution: 1. **Identify \( a \) and \( b \)**: - Here, \( a = 25 \) and \( b = 15 \). 2. **Apply the identity**: - According to the identity, we can rewrite \( 25^2 - 15^2 \) as: \[ (25 + 15)(25 - 15) \] 3. **Calculate \( a + b \)**: - Calculate \( 25 + 15 \): \[ 25 + 15 = 40 \] 4. **Calculate \( a - b \)**: - Calculate \( 25 - 15 \): \[ 25 - 15 = 10 \] 5. **Multiply the results**: - Now, substitute back into the expression: \[ (40)(10) = 400 \] ### Final Answer: \[ 25^2 - 15^2 = 400 \] ---
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