G8T1U2S9 Expansion on Algebraic Expressions (Practice Set #1)

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

• -x + 3y

• 5x - 2y

• 2x + 3y

• -4x + 3y

Answer explanation

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

Expand the binomial: (2x - 3)^3

• 8x^3 - 36x^2

  • +54x + 27

• 8x^3 + 36x^2

  • +54x - 27

• 8x^3 + 36x^2

  • +54x + 27

• 8x^3 - 36x^2

  • +54x - 27

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. Therefore, (2x + 3)^2 = (2x)^2 + 2(2x)(3) + 3^2 = 4x^2 + 12x + 9.

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

• 3y

• 5x^2, -2x^2

• 2xy

• 3x^2

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.

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

2(3x + 4)

• 5x + 8

• 6x + 8

• 6x + 4

• 3x + 8

Find the missing term in the expansion of (x + 2)^3: x^3 + 6x^2 + ? + 8

• 12x^2

• 10x^2

• 36x^2

• 4x^2

Answer explanation

To find the missing term in the expansion of (x + 2)^3, use the binomial theorem. The missing term is 3 * (x^2) * (2) = 6x^2. Therefore, the missing term is 6x^2, which corresponds to the choice 36x^2.

Apply the FOIL method to expand: (x + 2)(x - 3)

• x^2 - x - 6

• x^2 - 5

• x^2 - 1

• x^2 + 5

Answer explanation

To expand (x + 2)(x - 3) using FOIL, multiply the First terms (x*x), Outer terms (x*-3), Inner terms (2*x), and Last terms (2*-3). Simplify to get x^2 - x - 6.

Expand the binomial to a polynomial: (2x - 1)^3

• 8x^3 - 12x^2 + 6x - 1

• 6x^3 - 9x^2 + 4x - 1

• 8x^3 - 12x^2 + 6x + 1

• 4x^3 - 6x^2 + 3x - 1

Answer explanation

To expand (2x - 1)^3, we use the binomial theorem. The result is 8x^3 - 12x^2 + 6x - 1, which matches the correct answer choice.

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

• 16x^2 - 16x + 4

• 16x^2 - 8x + 4

• 8x^2 - 16x + 4

• 8x^2 - 8x + 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 = (4x)^2 - 2(4x)(2) + (2)^2 = 16x^2 - 16x + 4.

Find the missing term in the expansion of (y - 3)^3: y^3 - 9y^2 + ? - 27

• 27y

• 18y

• 9y

• 36y

Answer explanation

To find the missing term in the expansion of (y - 3)^3, we use the binomial theorem. The missing term is -27y, so the correct answer is 9y.

Simplify the expression: (6b^5 + 7)(6b^5 - 7)

• 6b^10 + 49

• 36b^10 - 49

• 6b^10 - 49

• 36b^10 + 49

Answer explanation

Combine like terms by adding the coefficients of 'a' and 'b': 2a - a = a, 3b + 4b = 7b. Therefore, the simplified expression is a + 7b.