Question

What is the simplest form of the expression (5x + 3xy + 4y) + (4x – 2xy – 2y)? A. x + xy + 2y B. x2 + xy + 2y C. 9x + 5xy + 2y D. 9x + 5xy + 6y E. 9x + xy + 2y

2. 5y + 2z + 3x2 – (2y – 2z + 4x) is equivalent to: F. 7y + 4z + 3x2 – 4x G. 3y + 3x2 – 4x H. 3y + 4z + 3x2 – 4x J. 3y + 4z + 7x K. 3y + 4z + 7x2

3. Which of the following polynomials is equivalent to (x – 1)(x + 1)(x – 1)? A. x2 – x + 1 B. x2 – x – 1 C. x3 – x2 – x + 1 D. x3 – x2 – x – 1 E. x3 – 2x2 – 2x + 1

4. What is the product (2a + 6)2? F. 2a2 + 12a + 36 G. 4a2 + 12a + 36 H. 4a2 + 36 J. 4a2 + 24a + 36 K. 4a2 – 36

5. Among the following arithmetic operations, which could the symbol ♣ represent given that the equation (6 ♣ 1)3 – (4 ♣ 1)2 = 200 is true? I. Subtraction II. Multiplication III. Division A. II only B. III only C. II and III only D. I and III only E. I, II, and III

Answer 1

1. E.
2. H.
3. C.
4. J.
5. C.

Answer 2

1). Option E

2). Option H

3). Option C

4). Option J

5). Option C

Explanation:

1). (5x + 3xy + 4y) + (4x - 2xy - 2y)

= (5x + 4x) + (3xy - 2xy) + (4y - 2y)

= 9x + xy + 2y

Option E. is the answer.

2). 5y + 2z + 3x²- (2y - 2z + 4x)

= 5y - 2y - 4x + 2z + 2z + 3x²

= 3y - 4x + 4z + 3x²

Option H is the answer.

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

= (x² - 1)(x - 1) [Since (a - b)(a + b) = a² - b²]

= x²(x - 1) - 1(x - 1)

= x³ - x² - x + 1

Option C is the answer.

4). (2a + 6)²

= 4a² + 24a + 36

[Since (a + b)² = a² - 2ab + b²]

Option J. is the answer.

5). For subtraction,

(6 - 1)³ - (4 - 1)²

= 5³ - 3²

= 125 - 9

= 116

But the result is 200 so operation subtraction is not the answer.

For Multiplication,

(6 × 1)³ - (4 × 1)²

= 6³ - 4²

= 216 - 16

= 200

For division,

(6 ÷ 1)³ - (4 ÷ 1)²

= 6³ - 4²

= 216 - 16

= 200

Therefore, Option C. is the answer.