# SAT PRATICE QUESTION USING ALGEBRAIC IDENTITIES

Problem 1 :

Which of the following is equivalent to

(1/m)2 - 2 (1/m) (1/n) + (1/n)2

(a) (1/√m - 1/√n)4     (b) (1/m  - 1/n)2

(c)  1/(m-n)2     (d)  2/(m2 - mn +n2)

Problem 2 :

(3x + 2y)2

If the expression above can be written as

ax2 + bxy + cy2

where a, b and c are constants, what is the value a + b +c ?

Problem 3 :

x2 + kx + 9 = (x + a)2

In the equation above k and a are positive constants. If the equation is true for all values of x, what is the value of k ?

Problem 4 :

2x (x - y) (x + y)

Which of the following is equivalent to the expression above ?

(a) 4x3 - 2xy2     (b)  2x3 + 2xy2

(c)  2x3 - 2xy2     (d)  2x3 - 4xy + 2xy2

Problem 5 :

If (x + 3) (x - 3) = 91, what is the value of x2?

Problem 6 :

The expression

(x + 1)/(x + 2) - (x - 2)/(x - 1)

is equivalent to which of the following ?

(a)  -5/(x + 2) (x - 1)    (b)  1/(x + 2) (x - 1)

(c)  3/(x + 2) (x - 1)    (b)  (2x2+3)/(x + 2) (x - 1)

Problem 7 :

Which of the following is equivalent to

(m + n - 1) (m + n +1) ?

(a) m2 + 2mn + n2 - 1      (b) m2 - 2mn + n2 - 1

(c) m2 - n2 - 1  (d) m2 - 2mn + n2 - 1

Problem 8 :

(a + b)2 - (a - b)2

The expression above is equivalent

(a)  2ab     (b) 4ab     (c)  4ab + b2      (d)  2a2 + 2b2

Problem 9 :

(x - c)2 = x + 3

If c = 3, what is the solution set of the equation above ?

(a)  {1}    (b)  {6}     (c)  {1, 6}    (d)  {-3, 1, 6}

Problem 10 :

The following is equivalent form of

(1.5x - 2.4)2 - (5.2x2 - 6.4) ?

Solution

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