IDENTIFY LIKE AND UNLIKE TERMS

State whether a given pair of terms is of like or unlike terms.

Problem 1 :

-7x, 5/2x

Solution :

-7x, 5/2x are having same variables.

So, -7x, 5/2x are like terms.

Problem 2 :

1, 100

Solution :

1, 100 are constants.

These are like terms

Problem 3 :

-29x, -29y

Solution :

-29x, -29y are having different variables.

So, they are unlike terms.

Problem 4 :

14xy, 42yx

Solution :

14xy, 42yx are having same variables.

So, they are like terms.

Problem 5 :

4m²p, 4mp²

Solution :

4m²p, 4mp² are not same variables.

So, they are unlike terms.

Problem 6 :

12xz, 12x²z²

Solution :

12xz, 12x²z² are not having different variables.

So, they are unlike terms.

Problem 7 :

Identify like terms in the following :

-xy², -4yx², 8x², 2xy², 7y, -11x², -100x, -11yx, 20x²y, -6x², y, 2xy, 3x

Solution :

The terms which are having xy² :

-xy² and 2xy²

The terms which are having x²y :

-4yx², 20x²y

The terms which are having x² :

8x²,  -11x²,- 6x²

The terms which are having xy :

-11yx, 2xy

The terms which are having x :

3x and -100x

The terms which are having y :

7y and y

Problem 8 :

10pq, 7p, 8q, -p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Solution :

The terms which are having pq :

10pq, -7qp, 78qp

The terms which are having p :

7p, 2405p

The terms which are having q :

8q, -100q

The terms which are having p²q² :

-p²q²,12q²p²

Terms don't have any variable :

-23, 41

The terms which are having p²q :

13p²q, qp²

The terms which are having p² :

-5p², 701p²

Problem 9 :

Let A = 4x + 8 and B = 6 + 8x, what is A + B?

Solution :

A = 4x + 8 and B = 6 + 8x

A + B = 4x + 8 + 6 + 8x

Combining the like terms, we get

= 4x + 8x + 8 + 6

= 12x + 14

Problem 10 :

Let X = 3x + 5 + 2x and Y = 4 + 7x + 1. What is X + Y ?

Solution :

X = 3x + 5 + 2x and Y = 4 + 7x + 1

X + Y = 3x + 5 + 2x + 4 + 7x + 1

Combining the like terms, weget

= 3x + 2x + 7x + 4 + 1

= 12x + 5

Problem 11 :

Julian says the expressions 3 + 3(2a + 2) and 9a + 9 are equivalent. Is she correct ? How do you know ?

Solution :

Simplifying 3 + 3(2a + 2)

= 3 + 3(2a + 2)

Distributing 3, we get

= 3 + 6a + 6

= 6a + 9

6a + 9 is not equivalent to 9a + 9.

Problem 12 :

To solve for the perimeter of a polygon, one must find the sum of all side. Look at the equilateral triangle below. What is the perimeter ?

Solution :

Since it is equilateral triangle all three sides will be equal.

Perimeter of triangle = 4x + 2 + 4x + 2 + 4x + 2

= 4x + 4x + 4x + 2 + 2 + 2

= 12x + 8

So, the perimeter of the triangle is 12x + 8.

Problem 13 :

To solve for the perimeter of a polygon, one must find the sum of all side. Look at the equilateral triangle below. What is the perimeter ?

Solution :

Length of the rectangle = 6x + 7

Width = 3x

Perimeter of the rectangle = 2(length + width)

= 2(6x + 7 + 3x)

= 2(9x + 7)

Distributing 2, we get

= 18x + 14

Problem 14 :

The area of Sandbox B is 4 square feet greater than the area of Sandbox A. Write and simplify an expression for the width w of Sandbox B.

Solution :

Area of sand box A = 4x (2x + 3)

Area of sand box B = w(2x + 1)

Area of sandbox B = 4x(2x + 3) + 4

w(2x + 1) = 4x(2x + 3) + 4

w = 4x(2x + 3)/(2x + 1) + 4/(2x + 1)

Problem 15 :

The candles shown have the same volume. Write and simplify an expression for the height of the cone-shaped candle.

Solution :

Volume of cylinder = πr² h

r = x and h = x + 4

= πx² (x + 4) -------(1)

Volume of cone shaped candle = (1/3) πr² h

= (1/3) π(2x)² h

= π(4x² h/3) -------(2)

Given that the volumes are equal, then

πx² (x + 4) = π(4x² h/3)

h = πx² (x + 4)(3/4πx²)

= (3/4) (x + 4)

Problem 16 :

The expression 12 + x + 4 represents the perimeter of a triangle. Simplify the expression.

Solution :

Perimeter of a triangle = 12 + x + 4

Simplifying the expression, we get

= 16 + x

Problem 17 :

Which expression is equivalent to 5(n − 8) + 4n?

a) 49n     b) 9n + 40    c) 9n − 40     d) 5n − 40

Solution :

= 5(n − 8) + 4n

= 5n - 40 + 4n

= 5n + 4n - 40

= 9n - 40

So, option c is correct.

Problem 18 :

A case of Scout cookies has 10 cartons. A carton has 12 boxes. The amount you earn on a whole case is 10(12x) dollars.

a. What does x represent?

b. Simplify the expression.

Solution :

a. The variable x represents the earnings (or price) per single box of cookies.

b. The simplified expression is 120x.