G8T1U2S8 Expansion on Algebraic Expressions (For Drill #2)

Simplify the expression: 3x + 2y - 4x + y

• 2x + 3y

• -4x + 3y

• -x + 3y

• 5x - 2y

Answer explanation

Combine like terms by adding the coefficients of x and y separately: 3x - 4x = -x, 2y + y = 3y. Therefore, the simplified expression is -x + 3y.

Expand the following binomial: (2x + 3)^2

• 4x^2 + 12x + 9

• 2x^2 + 6x + 9

• 4x^2 + 12x - 9

• 4x^2 + 6x + 9

Answer explanation

To expand (2x + 3)^2, apply the formula (a + b)^2 = a^2 + 2ab + b^2. In this case, a = 2x and b = 3. So, (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9. Therefore, the correct expansion is 4x^2 + 12x + 9.

Identify the like terms in the expression: 5x^2 + 3xy - 2x^2 + 4y

• 5x^2, -2x^2

• 3xy, -2x^2

• 5x^2, 4y

• 5x^2, 3xy

Answer explanation

The like terms in the expression are 5x^2 and -2x^2 because they both have the same variable raised to the same power, which is x^2.

Apply the Distributive Property of Multiplication over Addition [DPMA].

2(3x - 4)

• 6x - 8

• 3x - 8

• 5x - 8

• 6x - 4

Answer explanation

To apply the Distributive Property of Multiplication over Addition, distribute 2 to both terms inside the parentheses: 2(3x) - 2(4) = 6x - 8. Therefore, the correct answer is 6x - 8.

Explain the concept of Expansion on Algebraic Expansion

• Expansion involves subtracting terms within parentheses

• Expansion in algebra refers to the process of multiplying out the terms within parentheses and combining like terms to simplify the expression.

• Expansion in algebra is the process of dividing terms within parentheses

• Expansion refers to adding terms within parentheses without simplifying

Answer explanation

Expansion in algebra refers to the process of multiplying out the terms within parentheses and combining like terms to simplify the expression.

Evaluate the expanded form of (x + 3)(x - 3)

• x^2 - 9

• x^2 - 6

• x^2 - 5

• x^2 + 9

Answer explanation

To expand (x + 3)(x - 3), we use the FOIL method: First, Outer, Inner, Last. This simplifies to x^2 - 9, so the correct answer is x^2 - 9.

Find the like terms in the expression: 2x + 5xy - 3x + 2y

• 3xy

• 2x, -3x

• 5x^2

• 2xy

Answer explanation

The like terms in the expression are 2x and -3x because they both have the same variable 'x' raised to the power of 1.

Expand the binomial: (4x - 2)^2

• 16x^2 - 16

• 16x^2 - 8

• 16x^2 - 4x

• 16x^2 - 16x + 4

Answer explanation

To expand (4x - 2)^2, apply the formula (a - b)^2 = a^2 - 2ab + b^2. In this case, a = 4x and b = 2. Therefore, (4x - 2)^2 = 16x^2 - 16x + 4, which matches the correct answer choice.

Identify the like terms in the expression: 3x^2 + 2xy - 4x^2 + 5y

• 3x^2, -4x^2

• 2xy, 5y

• 3x^2, 2xy

• 3x^2, 5y

Answer explanation

The like terms in the expression are 3x^2 and -4x^2 because they both have the same variable raised to the same power, which is x^2.

Calculate the result of the special product (a + b)^2

• a^2 + 2ab + b^2

• 2ab

• a^2 + b^2

• a^2 - b^2

Answer explanation

The correct choice is a^2 + 2ab + b^2, which is the result of expanding (a + b)^2 using the formula (a + b)^2 = a^2 + 2ab + b^2.