# 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

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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