Question 1

The following algebraic expression $-7 x y+2 x$ can be classified as:
A) monomial
B) binomial
C) trinomial
D) multinomial
E) All choices are incorrect

Accepted Answer

The expression $-7xy + 2x$ consists of two terms, making it a binomial.

Question 2

Simplify and collect like terms: 9x - [4y - 3(x - y)]
A) 12 x + 7y
B) 6x - 7y
C) 6x + 7y
D) 12x - 7y
E) 9x - 7y

Accepted Answer

D

Question 3

Simplify the following: (2x³)⁵ A) 10x¹⁵ B) 32x⁸ C) 32x¹⁵ D) 2x¹⁵ E) 2x⁸

Accepted Answer

When raising a power to another power, you multiply the exponents. So, (2x^3)^5 = 2^5 * (x^3)^5 = 32x^15.

Question 4

Simplify and collect like terms: $\frac{12 x y-6 y^{2}}{3 y}$ A) 4x + 2y B) 4xy - 2y C) 4xy + 2y² D) 4x - 2y E) 4xy - 2y²

Accepted Answer

The answer of Simplify and collect like terms: \(\frac{12 x...

Question 5

2(b - 2) - (b - 2) =
A) b + 6
B) 3b - 2
C) 3b + 2
D) b - 2
E) b - 6

Accepted Answer

Expanding and simplifying the given expression: 2(b - 2) - (b - 2) = 2b - 4 - b + 2 = b - 2.

Question 6

Simplify and collect like terms: 4x + 5 - 2.1(x - 7)x8
A) -1.6x - 14.075
B) -1.6x - 15.325
C) 2.6x + 15.325
D) 2.6x - 14.075
E) -1.6x + 15.325

Accepted Answer

The answer of Simplify and collect like terms: 4x +...

Question 7

Simplify and collect like terms: 3(x - 2y)(2x + y) A) 6x² - 6xy - 6y² B) 6x² + 10xy - 6y² C) 6x² - 9xy - 6y² D) 6x² - 9xy + 6y² E) 6x² + 10xy + 6y²

Accepted Answer

First, distribute the 3 into the parentheses: 3(x - 2y)(2x + y) = 3(2x^2 + xy - 4xy - 2y^2) = 6x^2 - 9xy - 6y^2.

Question 8

Simplify the following: (x⁵)⁴ A) x⁹ B) x²⁰ C) x D) x^-1 E) x⁰

Accepted Answer

When raising a power to another power, you multiply the exponents: (x^5)^4 = x^(5*4) = x^20.

Question 9

Simplify the following: b⁸ / b² A) b⁴ B) b¹⁰ C) b¹⁶ D) b^-6 E) b⁶

Accepted Answer

The given expression simplifies to b^18 / b^12, which equals b^(18-12) = b^6, matching choice E.

Question 10

Simplify the following: (a²) (a^-6) (a³) A) a¹¹ B) a C) a^-36 D) a^-1 E) a^-5

Accepted Answer

The answer of Simplify the following: (a²) (a^-6) (a³) A) a¹¹ B)...

Question 11

Simplify: $\frac{6 a+9}{3}-4(a-1)$
A) -2a + 13
B) -2a - 1
C) -2a + 7
D) 2a + 7
E) 2a - 1

Accepted Answer

First, simplify the fraction by dividing both terms in the numerator by the denominator: $\frac{6a}{3} + \frac{9}{3} = 2a + 3$. Then, distribute the -4 across the terms in the parentheses: $-4(a-1) = -4a + 4$. Combine like terms: $2a + 3 - 4a + 4 = -2a + 7$.

Question 12

Simplify the following: y⁸ / y⁵ A) y¹³ B) y³ C) y^-40 D) y⁴⁰ E) y^-13

Accepted Answer

The answer of Simplify the following: y⁸ / y⁵ A) y¹³ B)...

Question 13

Simplify the following: a² x a⁶ x a A) a⁸ B) a⁷ C) a⁹ D) a¹² E) a¹³

Accepted Answer

When multiplying powers with the same base, you add the exponents: 2 + 6 + 1 = 9, so the expression simplifies to a^9.

Question 14

The following numerical coefficient(s) of $3 a b^{2}-4 a^{2}+2$ , is/are:
A) -4,2
B) 3,4
C) 2
D) 3,-4,2
E) 3,-4

Accepted Answer

The numerical coefficients are the numbers in front of the variables in each term of the expression. In $3ab^2 - 4a^2 + 2$, the coefficients are 3 for $3ab^2$, -4 for $-4a^2$, and 2 for the constant term.

Question 15

Simplify the following: $\frac{\left({x^{5}}\right)\left(x\right)\left(x^{-3}\right)}{x^{-4}}$ A) x^-1 B) x⁶ C) x^-2 D) x⁷ E) x²

Accepted Answer

To simplify the expression, we use the properties of exponents. The expression is $\frac{x^5 \cdot x \cdot x^{-3}}{x^{-4}}$. First, we add the exponents in the numerator: $5 + 1 - 3 = 3$. Then, we subtract the exponent in the denominator from the sum we just found: $3 - (-4) = 3 + 4 = 7$. Thus, the simplified expression is $x^7$, which corresponds to choice D.

Question 16

Simplify and collect like terms: -a + (2b - c) - (a -b +c)
A) -2a + 3b - 2c
B) -2a + b - 2c
C) 3b - 2c
D) -2a + 3b
E) -2a + 2b - 2c

Accepted Answer

-a + (2b - c) - (a -b +c) = -a + 2b - c - a + b - c = -2a + 3b - 2c

Question 17

The following algebraic expression $3 a b^{2}-4 a^{2}+2$ , can be classified as:
A) monomial
B) binomial
C) trinomial
D) multinomial
E) All choices are incorrect

Accepted Answer

The expression $3 a b^{2}-4 a^{2}+2$ consists of three terms: $3 a b^{2}$, $-4 a^{2}$, and $2$, making it a trinomial.

Question 18

Evaluate: L(1 - d₁)(1 - d₂) for L = $1000, d₁ = 0.30, and d₂ = 0.20. A) $440.00 B) $500.00 C) $1785.71 D) $560.00 E) $600.00

Accepted Answer

The correct evaluation is done by substituting the given values into the formula: L(1 - d₁)(1 - d₂) = $1000 * (1 - 0.30) * (1 - 0.20) = $1000 * 0.7 * 0.8 = $560.

Question 19

Simplify and collect like terms: $\frac{10 x y^{2}-15 x^{3} y^{2}+25 x y^{4}}{5 x y}$ A) 2y² - 3x²y + 5y³ B) 2xy - 3x²y + 5y³ C) 2y - 3x²y + 5y D) 2y - 3x² + 5y E) 2y - 3x²y + 5y³

Accepted Answer

The answer of Simplify and collect like terms: \(\frac{10 x...

Question 20

Simplify and collect like terms: 1 - (3x - xy + y) - (-x + y - 5xy)
A) 1 - 2x - 2y - 6xy
B) 1 - 2x - 2y + 6xy
C) 1 - 4x - 2y + 6xy
D) 1 - 2x - 2y + 4xy
E) 1 - 4x - 2y - 6xy

Accepted Answer

Distribute the negative signs and combine like terms: 1 - 3x + xy - y + x - y + 5xy = 1 - 2x - 2y + 6xy.

Quiz 2: Review and Applications of Algebra

The following algebraic expression $-7 x y+2 x$ can be classified as:

Simplify and collect like terms: 9x - [4y - 3(x - y) ]

Simplify the following: (2x³) ⁵

Simplify and collect like terms: $\frac{12 x y-6 y^{2}}{3 y}$

2(b - 2) - (b - 2) =

Simplify and collect like terms: 4x + 5 - 2.1(x - 7) x8

Simplify and collect like terms: 3(x - 2y) (2x + y)

Simplify the following: (x⁵) ⁴

Simplify the following: b⁸ / b²

Simplify the following: (a²) (a^-6) (a³)

Simplify: $\frac{6 a+9}{3}-4(a-1)$

Simplify the following: y⁸ / y⁵

Simplify the following: a² x a⁶ x a

The following numerical coefficient(s) of $3 a b^{2}-4 a^{2}+2$ , is/are:

Simplify the following: $\frac{\left({x^{5}}\right) \left(x\right) \left(x^{-3}\right) }{x^{-4}}$

Simplify and collect like terms: -a + (2b - c) - (a -b +c)

The following algebraic expression $3 a b^{2}-4 a^{2}+2$ , can be classified as:

Evaluate: L(1 - d₁) (1 - d₂) for L = $1000, d₁ = 0.30, and d₂ = 0.20.

Simplify and collect like terms: $\frac{10 x y^{2}-15 x^{3} y^{2}+25 x y^{4}}{5 x y}$

Simplify and collect like terms: 1 - (3x - xy + y) - (-x + y - 5xy)

Quiz 2: Review and Applications of Algebra

The following algebraic expression −7xy+2x-7 x y+2 x−7xy+2x can be classified as:

Simplify and collect like terms: 9x - [4y - 3(x - y) ]

Simplify the following: (2x3) 5

Simplify and collect like terms: 12xy−6y23y\frac{12 x y-6 y^{2}}{3 y}3y12xy−6y2​

2(b - 2) - (b - 2) =

Simplify and collect like terms: 4x + 5 - 2.1(x - 7) x8

Simplify and collect like terms: 3(x - 2y) (2x + y)

Simplify the following: (x5) 4

Simplify the following: b8 / b2

Simplify the following: (a2) (a-6) (a3)

Simplify: 6a+93−4(a−1) \frac{6 a+9}{3}-4(a-1) 36a+9​−4(a−1)

Simplify the following: y8 / y5

Simplify the following: a2 x a6 x a

The following numerical coefficient(s) of 3ab2−4a2+23 a b^{2}-4 a^{2}+23ab2−4a2+2 , is/are:

Simplify the following: (x5) (x) (x−3) x−4\frac{\left({x^{5}}\right) \left(x\right) \left(x^{-3}\right) }{x^{-4}}x−4(x5) (x) (x−3) ​