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

Simplify: x+1...

Question

Simplify: $(x + 1) (x - 1) (2 x - 3)$

A

2 x^{3} - 3 x^{2} - 3 x + 3

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B

2 x^{3} - 3 x^{2} + 3 x + 3

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C

2 x^{3} + 3 x^{2} + 2 x + 3

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D

2 x^{3} - 3 x^{2} - 2 x + 3

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Solution

The correct option is D $2 x^{3} - 3 x^{2} - 2 x + 3$
(x + 1)(x - 1)(2x - 3)
Using the identity $(a + b) (a - b) = a^{2} - b^{2}$ for $(x + 1) (x - 1)$
$= (x^{2} - 1^{2}) \times (2 x - 3)$
$= x^{2} (2 x - 3) - (1) (2 x - 3)$
$= 2 x^{3} - 3 x^{2} - 2 x + 3$

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Q. The number of real solutions of

(x - 1) (x + 1) (2 x + 1) (2 x - 3) = 15

A (x) = ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 2 x + 1 & 3 x + 1 2 x + 1 & 3 x + 1 & x + 1 3 x + 1 & x + 1 & 2 x + 1 \end{matrix} ∣ ∣ ∣ ∣

\int_{0}^{1} A (x) d x =

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