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Simplify the expression:
(c + d)2 - (c - d)2
- a)4cd
- b)(c2 + d2)
- c)2(c2+ d2)
- d)2cd
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Simplify the expression:(c + d)2- (c - d)2a)4cdb)(c2+ d2)c)2(c2+ d2)d)...
Formula Used :
x2 - y2 = (x + y) (x - y)
Calculation:
⇒ (c + d)2 - (c - d)2
⇒ (c + d + c - d) (c + d -(c - d))
⇒ 2c × (c + d - c + d)
⇒ 2c × 2d = 4cd
∴ The simplified value is 4cd.
Alternate Method
Formula Used :
(x + y)2 = x2 + y2 + 2xy
(x - y)
2 = x
2 + y
2 - 2xy
Calculation:
⇒ (c + d)2 - (c - d)2
⇒ c2 + d2 + 2cd - (
c
2 + d
2 - 2cd)
⇒ c
2 + d
2 + 2cd -
c
2
- d
2
+ 2cd
⇒
4cd∴ The simplified value is 4cd.
Most Upvoted Answer
Simplify the expression:(c + d)2- (c - d)2a)4cdb)(c2+ d2)c)2(c2+ d2)d)...
Explanation:
To simplify the given expression (c + d)2 - (c - d)2, we need to expand and simplify the terms.
Expansion:
(c + d)2 = c2 + 2cd + d2
(c - d)2 = c2 - 2cd + d2
Simplifying the expression:
(c + d)2 - (c - d)2
= (c2 + 2cd + d2) - (c2 - 2cd + d2)
= c2 + 2cd + d2 - c2 + 2cd - d2
= 4cd
Therefore, the simplified expression is 4cd, which is option 'A'.
To simplify the given expression (c + d)2 - (c - d)2, we need to expand and simplify the terms.
Expansion:
(c + d)2 = c2 + 2cd + d2
(c - d)2 = c2 - 2cd + d2
Simplifying the expression:
(c + d)2 - (c - d)2
= (c2 + 2cd + d2) - (c2 - 2cd + d2)
= c2 + 2cd + d2 - c2 + 2cd - d2
= 4cd
Therefore, the simplified expression is 4cd, which is option 'A'.
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Question Description
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