Mathematics
(x + 3) (x + 3) - (x - 2) (x - 2) is equal to:
10x + 5
10x - 5
5 - 10x
none of these
Identities
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Answer
Using the formula,
[∵(x + y) = x2 + y2 + 2xy]
And,
[∵(x - y) = x2 + y2 - 2xy]
(x + 3) (x + 3) - (x - 2) (x - 2)
⇒ [(x + 3)2] - [(x - 2)2]
⇒ [x2 + 32 + 2 x 3] - [x2 + 22 - 2 x 2]
⇒ [x2 + 9 + 6x] - [x2 + 4 - 4x]
⇒ x2 + 9 + 6x - x2 - 4 + 4x
⇒ (x2 - x2) + (9 - 4) + (6x + 4x)
⇒ 5 + 10x
⇒ 10x + 5
Hence, option 1 is the correct option.
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Statement 1: Cube of a binomial : (a - b)3 = a3 + 3a2b - 3ab2 - b3
Statement 2: (a - b)2 - (a + b)2 = 4ab.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.