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**Section - 1Distribute the following expressions.Ques 1: (x+ 2)(x- 3)Ans:** (x + 2 )(x -3 )= x

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Ques 5: x

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x(x â€” 2) = 0

x= 0

OR (x -2 ) = 0 -> x = 2

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Simplify the following expressions.

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After replacing the original numerator with (a + b)(a - b), we can cancel the (a - b) in the numerator with the (a - b) in the denominator:

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Because we have a common factor in both terms of the numerator, we can divide that factor out in order to simplify further. This is often a useful move when we are asked to add or subtract exponents with the same base:**Ques 14: **

Alternatively, we can introduce a new variable x defined as x = 2t â€” 1. In general, it is not a good idea to introduce more variables than strictly necessary, but in this case the new variable can make it easier to see how the math works:

We can then simplify the expression in terms of x:

And we then finish by replacing x with 2t - 1

x + 1 = (2t â€” 1) + 1 = 2t**Section - 4Simplify the following expressions.Ques 15: (A) 5 - x (B) x - 5 (C) x + 5Ans: **We can make this problem a lot simpler if we begin by factoring 3 out of both the nu-

merator and the denominator:

The answers are not fractions, so well have to get rid of the denominator. Factor the numerator:**Ques 16: Ans:** This might seem nearly impossible to factor down until we take out the common term: ab. Then, we are left with one of our familiar special products in the denominator:

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simplify before multiplying. Notice that x^{3} can be factored out of the numerator and x^{2} can be factored out of the denominator:

Notice now that we can cancel x^{2}, from the fraction. Also, we have (x^{2} - 1) in the numerator, which we can factor:

We donâ€™t have a match with any of the answer choices yet. None of the numerators in the answer choices have parenthetical expressions. We should multiply the numerator:

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