Extended Distributive Property Practice Problems & Worksheets

To solve this problem, we will expand the expression $(x-3)(x-6)$ using the distributive property, which involves the following steps:

• Step 1: Multiply the first terms of each binomial
  $(x)(x) = x^2$

• Step 2: Multiply the outer terms of the binomials
  $(x)(-6) = -6x$

• Step 3: Multiply the inner terms of the binomials
  $(-3)(x) = -3x$

• Step 4: Multiply the last terms of each binomial
  $(-3)(-6) = 18$

• Step 5: Combine all the products
  $x^2 - 6x - 3x + 18$

• Step 6: Combine like terms
  $-6x - 3x = -9x$, so we have
  $x^2 - 9x + 18$

Therefore, the expanded form of $(x-3)(x-6)$ is $\boxed{x^2 - 9x + 18}$.

Therefore, the solution to the problem is $x^2 - 9x + 18$. This corresponds to choice 1.

To solve the algebraic expression $(2y-3)(y-4)$, we will apply the distributive property, also known as the FOIL method for binomials. This involves multiplying each term in the first binomial by each term in the second binomial.

• Step 1: Multiply the first terms: $2y \times y = 2y^2$.
• Step 2: Multiply the outer terms: $2y \times -4 = -8y$.
• Step 3: Multiply the inner terms: $-3 \times y = -3y$.
• Step 4: Multiply the last terms: $-3 \times -4 = 12$.

Next, we combine all these results: $2y^2 - 8y - 3y + 12$.

Then, we combine the like terms $-8y$ and $-3y$ to get $-11y$.

Therefore, the expanded expression is $2y^2 - 11y + 12$.

This matches choice (3): $2y^2 - 11y + 12$.

Thus, the solution to the problem is $2y^2 - 11y + 12$.

To solve this problem, we'll apply the distributive property to expand the expression $(3x-1)(x+2)$. Below are the steps:

• Step 1: Distribute each term in the first binomial to each term in the second binomial:

$3x(x) + 3x(2) + (-1)(x) + (-1)(2)$

• Step 2: Calculate each term:

$3x^2 + 6x - x - 2$

• Step 3: Combine like terms:

$3x^2 + (6x - x) - 2 = 3x^2 + 5x - 2$

Thus, the expanded expression is $3x^2 + 5x - 2$.

The correct answer choice is $3x^2 + 5x - 2$, corresponding to choice id="4".

To solve the problem $(5x-2)(3+x)$, we will use the distributive property, specifically the FOIL (First, Outer, Inner, Last) method, to expand the expression:

• Step 1: Multiply the First terms: $5x \times 3 = 15x$.
• Step 2: Multiply the Outer terms: $5x \times x = 5x^2$.
• Step 3: Multiply the Inner terms: $-2 \times 3 = -6$.
• Step 4: Multiply the Last terms: $-2 \times x = -2x$.

Now combine all these products together:

$5x^2 + 15x - 2x - 6$

Combine the like terms $15x$ and $-2x$:

$5x^2 + (15x - 2x) - 6 = 5x^2 + 13x - 6$

Thus, the expanded form of the expression is $5x^2 + 13x - 6$.

Simplify this expression paying attention to the order of arithmetic operations. Exponentiation precedes multiplication whilst division precedes addition and subtraction. Parentheses precede all of the above.

Therefore, let's first start by simplifying the expressions within the parentheses. Then we can proceed to perform the multiplication between them:

$(3+20)\cdot(12+4)=\\ 23\cdot16=\\ 368$

Therefore, the correct answer is option A.