Algebraic Expressions and Equations

The following are the types of algebraic expressions, EXCEPT?

• Monomial

• Binomial

• Trinomial

• Polynomial

Answer explanation

There are three basic types of algebraic expressions. They are;

1. 1. Monomial-Which has only one non-zero term.

2. 2. Binomial-Which has two non-zero terms.

3. 3. Polynomial- Which has more than one non-zero term with non-negative integral exponents.

What is a variable in an algebraic expression?

• It is a value used with the variable term and is well defined.

• It is an unknown quantity which we need to evaluate equations.

• It is a term that has a definite value.

• None of the above

Answer explanation

A variable is an unknown quantity which we need to evaluate by solving the given algebraic equation.

What is a coefficient in an algebraic expression?

• It is a value used with the variable term and is well defined.

• It is an unknown quantity which we need to evaluate equations.

• It is a term that has a definite value.

• None of the above

Answer explanation

Coefficient is a constant value used with the variable term and is well defined.

In the equation 5x-3, what is the variable?

• 3

• 5

• x

• 0

Answer explanation

In the above expression (i.e. 5x – 3),

• x is a variable, whose value is unknown to us which can take any value.

• 5 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.

• 3 is the constant value term that has a definite value.

In the equation 21x+4, what is the coefficient?

• 4

• 21

• x

• 0

Answer explanation

In the above expression (i.e. 21x + 4),

• x is a variable, whose value is unknown to us which can take any value.

• 21 is known as the coefficient of x, as it is a constant value used with the variable term and is well defined.

• 4 is the constant value term that has a definite value.

In the equation 21x²+3x-1, what is the constant?

• -1

• 21

• x

• 3

Answer explanation

In the above expression (i.e. 21x² + 3x - 1),

• x² and x are the variables, whose value is unknown to us which can take any value.

• 21 and 3 are known as the coefficient of x² and x, as it is a constant value used with the variable term and is well defined.

• -1 is the constant value term that has a definite value.

Add 3x + 5y – 6z from x – 4y + 2z

• 3x+2y-3z

• 4z-4x+y

• 2x+4y-z

• 4x + y – 4z

Answer explanation

3x + 5y – 6z and x – 4y + 2z

= (3x + 5y – 6z) + (x – 4y + 2z)

= (3x + x) + (5y – 4y) + (-6z + 2z)

= 4x + y – 4z

Ans. 4x + y – 4z

Simplify this given 50x³ – 20x + 8x + 21x³ – 3x + 15x – 41x³.

• 30x³

• 25x³

• 35x³

• 40x³

Answer explanation

50x³ – 20x + 8x + 21x³ – 3x + 15x – 41x³

= (50x³ + 21x³ - 41x³) + (-20x + 8x - 3x + 15x)

= (30x³) + (0x)

= 30x³

Therefore, 30x³ is the answer.

Subtract 3y+xy from -5y+12xy

• 8y-11xy

• 8y+11xy

• -8y+11xy

• 19xy²

Answer explanation

(3y + xy) - (-5y + 12xy)

= 3y - (-5y) + (12xy-xy)

= -8y + 11xy

Therefore, -8y + 11xy is the answer.

Add this equation 2x+5xy+2xy.

• -2x+7xy

• -2x+8xy

• 2x+8xy

• 2x+7xy

Answer explanation

2x+5xy+2xy
= 2x + (5 + 2) xy

= 2x + (7) xy

= 2x + 7xy

Therefore, the answer is 2x + 7xy.