ALGEBRAIC IDENTITIES WORKSHEET FOR SAT

Problem 1 :

(3x + 2y)2

In the expression above can be written as ax2 + bxy + cy2, where a, b and c are constants, where a + b + c ?

Solution

Problem 2 :

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 ?

a)  0      b) 3     c)  6       d)  9

Solution

Problem 3 :

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

Solution

Problem 4 :

If (c + d) = -5 and (c - d) = -12, then what is the value of c2 - d2?

Solution

Problem 5 :

If (mx + c) (nx + 3) = 12x2 + 5x - 3 for all values of x, where m, n and c are constants, what is the value of m + n ?

a) 7      b)  8     c)  12       d)  13

Solution

Problem 6 :

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

Solution

Problem 7 :

If (x + y)2 - (x - y)2 = 60 and x and y are positive integers, which of the following could be the value of x + y ?

a)  6      b)  8       c)  10    d)  12

Solution

Problem 8 :

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

The expression above equivalent to which of following ?

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

Solution

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}

Solution

Problem 10 :

x2 - y2 = 48

x + y = 12

If (x, y) is the solution to the system of equations above, what is the value of xy? 

a)  28    b)  32    c)  45    d)  64

Solution

Answer Key

1)  the answer is 25.

2)  the value of k is 6.

3)  the value of x2 is 100.

4)  the value of c2 - dis 60.

5) the value of m + n is 7

6)  the value of a + b + c is 55.

7)  the value of x + y is 8.

8)   4ab

9)  the values of x are {1, 6}

10)  xy = 32.

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