8th Grade Math Algebra Quiz

1. Is it true? (3x-7)^2 = 18x^2 - 74x + 97

True

False

The given statement is false because when we expand (3x-7)^2, we get 9x^2 - 42x + 49, which is not equal to 18x^2 - 74x + 97. Therefore, the correct answer is false.

Explanation

The given statement is false because when we expand (3x-7)^2, we get 9x^2 - 42x + 49, which is not equal to 18x^2 - 74x + 97. Therefore, the correct answer is false.

2. 3X (-5X+x^2-3) =

3x^3 - 15x^2 - 9x

4x^3-15x^2-8x

3x^3-15^2-2x

4x^3-15x^2-9x

The given equation is a multiplication of 3x with the expression (-5x + x^2 - 3). To simplify the equation, we distribute the 3x to each term inside the parentheses. This results in 3x*(-5x) + 3x*(x^2) + 3x*(-3), which simplifies to -15x^2 + 3x^3 - 9x. Therefore, the correct answer is 3x^3 - 15x^2 - 9x.

Explanation

The given equation is a multiplication of 3x with the expression (-5x + x^2 - 3). To simplify the equation, we distribute the 3x to each term inside the parentheses. This results in 3x*(-5x) + 3x*(x^2) + 3x*(-3), which simplifies to -15x^2 + 3x^3 - 9x. Therefore, the correct answer is 3x^3 - 15x^2 - 9x.

3. (6x-5)(3x+1)

9x - 9x - 5

18x^2 - 6x - 7

18x^2 - 9x - 5

18x^2 - 8x - 7

The given expression is a product of two binomials: (6x-5) and (3x+1). To find the product, we can use the distributive property. Multiplying the first terms of each binomial gives us 6x * 3x = 18x^2. Multiplying the outer terms gives us 6x * 1 = 6x. Multiplying the inner terms gives us -5 * 3x = -15x. Finally, multiplying the last terms gives us -5 * 1 = -5. Combining like terms, we get 18x^2 - 9x - 5.

Explanation

The given expression is a product of two binomials: (6x-5) and (3x+1). To find the product, we can use the distributive property. Multiplying the first terms of each binomial gives us 6x * 3x = 18x^2. Multiplying the outer terms gives us 6x * 1 = 6x. Multiplying the inner terms gives us -5 * 3x = -15x. Finally, multiplying the last terms gives us -5 * 1 = -5. Combining like terms, we get 18x^2 - 9x - 5.

4. (6x+1) (6x-1)

36x^2 + 1

36x^2 - 1

12x^2 -+ 1

12x - 1

The given expression is a product of two binomials, (6x+1) and (6x-1). When we multiply these two binomials using the FOIL method, we get 36x^2 - 1. Therefore, the correct answer is 36x^2 - 1.

Explanation

The given expression is a product of two binomials, (6x+1) and (6x-1). When we multiply these two binomials using the FOIL method, we get 36x^2 - 1. Therefore, the correct answer is 36x^2 - 1.

5. Is it true? (4x-7)^2 = 16x^2 - 56x + 49

True

False

The given equation (4x-7)^2 = 16x^2 - 56x + 49 is true. This can be proven by expanding the square of the binomial (4x-7)^2, which results in 16x^2 - 56x + 49. Therefore, the equation is correct.

Explanation

The given equation (4x-7)^2 = 16x^2 - 56x + 49 is true. This can be proven by expanding the square of the binomial (4x-7)^2, which results in 16x^2 - 56x + 49. Therefore, the equation is correct.

6. (8x+1) (8x-1) = 73x^2 + 1 Equation above is incorrect.

True

False

The equation (8x+1)(8x-1) = 73x^2 + 1 is incorrect because the product of (8x+1) and (8x-1) does not equal 73x^2 + 1. Therefore, the correct answer is True, indicating that the equation is indeed incorrect.

Explanation

The equation (8x+1)(8x-1) = 73x^2 + 1 is incorrect because the product of (8x+1) and (8x-1) does not equal 73x^2 + 1. Therefore, the correct answer is True, indicating that the equation is indeed incorrect.

7. (3m^2-7m+8)(m-2)

3m^3 - 13m^2 + 22m - 16

3m^3 - 13m^2 + 25m - 14

4m^3 - 13m^2 + 22m - 16

3m^3 - 13m + 22m - 16

The given expression is a product of two binomials. To find the product, we can use the distributive property. We multiply each term of the first binomial, (3m^2-7m+8), by each term of the second binomial, (m-2). After simplifying, we get 3m^3 - 13m^2 + 22m - 16. Therefore, the correct answer is 3m^3 - 13m^2 + 22m - 16.

Explanation

The given expression is a product of two binomials. To find the product, we can use the distributive property. We multiply each term of the first binomial, (3m^2-7m+8), by each term of the second binomial, (m-2). After simplifying, we get 3m^3 - 13m^2 + 22m - 16. Therefore, the correct answer is 3m^3 - 13m^2 + 22m - 16.

8. If pmq = p+q + pq, then what is the value of 8 m 2?

10

12

14

26

The equation p×q = p+q + pq suggests that the multiplication of two numbers is equal to the sum of the two numbers plus their product. To find the value of 8 × 2, we substitute p = 8 and q = 2 into the equation. This gives us 8 × 2 = 8 + 2 + (8 × 2), which simplifies to 26.

Explanation

The equation p×q = p+q + pq suggests that the multiplication of two numbers is equal to the sum of the two numbers plus their product. To find the value of 8 × 2, we substitute p = 8 and q = 2 into the equation. This gives us 8 × 2 = 8 + 2 + (8 × 2), which simplifies to 26.

9. Match the expression to its term.

(b-5)

4m-3

Submit

10. If a*b = 2a-3b+ab, then what is 3*5+5*3?

17

18

21

22

To find the value of 3*5+5*3, we can substitute the values of a and b into the given equation. Let's assign a=3 and b=5 for 3*5. Plugging these values into the equation a*b = 2a-3b+ab, we get 3*5 = 2(3) - 3(5) + (3)(5). Simplifying this expression, we have 6 - 15 + 15 = 6. For 5*3, we have a=5 and b=3, 5*3 = 2*5 - 3*3 + 3*5 = 16. Adding both we get 22.

Explanation

To find the value of 3*5+5*3, we can substitute the values of a and b into the given equation. Let's assign a=3 and b=5 for 3*5. Plugging these values into the equation a*b = 2a-3b+ab, we get 3*5 = 2(3) - 3(5) + (3)(5). Simplifying this expression, we have 6 - 15 + 15 = 6. For 5*3, we have a=5 and b=3, 5*3 = 2*5 - 3*3 + 3*5 = 16. Adding both we get 22.