SIMPLIFY BY COMBINING LIKE TERMS WORKSHEET

Simplify combining like terms :

Problem 1 :

21b – 32 + 7b – 20b

Solution

Problem 2 :

–z² + 13z² – 5z + 7z³ – 15z

Solution

Problem 3 :

p – (p – q) – q – (q – p)

Solution

Problem 4 :

3a – 2b – ab – (a – b + ab) + 3ab + b – a

Solution

Problem 5 :

5x²y – 5x² + 3yx² – 3y² + x² – y² + 8xy² – 3y²

Solution

Problem 6 :

(3y² + 5y – 4) – (8y – y² – 4)

Solution

Add the following :

Problem 7 :

3mn, -5mn, 8mn, -4mn

Solution

Problem 8 :

t – 8tz, 3tz – z, z - t

Solution

Problem 9 :

-7mn + 5, 12mn + 2, 9mn – 8, -2mn - 3

Solution

Problem 10 :

a + b – 3, b – a + 3, a – b + 3

Solution

Subtract the following :

Problem 11 :

-5y² from y²

Solution

Problem 12 :

6xy from -12xy

Solution

Problem 13 :

(a – b) from (a + b)

Solution

Problem 14 :

a(b – 5) from b(5 – a)

Solution

Problem 15 :

-m² + 5mn from 4m² – 3mn + 8

Solution

Problem 1 :

(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 2 :

5x + 12 = (10x + 3c) / 2

In the equation above, c is a constant. For what value of c will the equation have infinitely many solutions ?

Solution

Problem 3 :

In the xy plane, the points (c, 2d) and (c + 3, 4d) lie on the line with equation y = mx + b, where m and b are nonzero constants/ What is the value of d/m ?

a)  2/3    b)  1    c)  3/2    d)  2

Solution

Problem 4 :

If the expression (1/4) x² + 3x + 9 is rewritten in the form 1/4 (x + a)², where a is a positive constant. What is the value of a ?

a)   3/2    b)  3     c)   6       d) 2√3

Solution

Problem 5 :

In the xy-plane, the line defined by the equation y = 3x - 5 passes through the vertex of a parabola with x-intercepts 3 and 15. What is the y-coordinate of the vertex of the parabola ?

Solution

Problem 6 :

9x³ - kx + 4

In the polynomial above, k is an integer. If 3x - 2 is a factor of the polynomial. What is the value of k ?

Solution

Problem 7 :

The function f a nd g are defined by f(x) = x² + 2 and g(x) = 4x  - 3. If a > 0, for what value of a does g(f(a)) = 41 ?

Solution

Problem 8 :

In the xy-plane the line with equation y = ax + b, where a and b are constants, intersects the line with equation y = 2bx + a at the point (3, 4) .If b ≠ 0, what is the value of a/b ?

a) 2/3   b) 3/4   c)  5/2    d) 7/3

Solution

Problem 9 :

y = x² - k

In the equation above, k is a constant. If the graph of the equation in the xy-plane is a parabola with x-intercepts of -4 and 4, what is the minimum value of y in terms of k ?

Solution

Problem 10 :

In the xy - plane the points (a, 7) and (b, 12) lie on the graph of y = x² + 3. What is the minimum possible value of a + b ?

a)  -5       b)  -1    c)   1    d)  5

Solution

Identify the numerical coefficients of terms (other than constants) in the following expressions :

Problem 1 :

5 – 3t²

Solution

Problem 2 :

1 + t + t² + t³

Solution

Problem 3 :

x + 2xy + 3y

Solution

Problem 4 :

100m + 1000n

Solution

Problem 5 :

-p²q² + 7pq

Solution

Problem 6 :

1.2 a + 0.8 b

Solution

Problem 7 :

3.14 r²

Solution

Problem 8 :

2(l + b)

Solution

Problem 9 :

0.1 y + 0.01 y²

Solution

Identify terms which contain x and give the coefficients of x.

Problem 1 :

y²x + y

Solution

Problem 2 :

13y² – 8yx

Solution

Problem 3 :

x + y + 2

Solution

Problem 4 :

5 + z + zx

Solution

Problem 5 :

1 + x + xy

Solution

Problem 6 :

12xy² + 25

Solution

Problem 7 :

7x + xy²

Solution

Identify terms which contain y² and give the coefficients of y².

Problem 1 :

8 – xy²

Solution

Problem 2 :

5y² + 7x

Solution

Problem 3 :

2x²y – 15xy² + 7y²

Solution