Extended Distributive Property Practice Problems & Worksheets

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.

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 $5x^2 + 13x - 6$.

To solve this problem, we'll use the distributive property, also known as the FOIL method when dealing with two binomials.

Let's expand the expression $(7+b)(a+9)$:

• First, apply the distributive property by multiplying each term in the first binomial by each term in the second binomial. This means we will have four operations:
• Step 1: Multiply $7$ by $a$. This gives $7a$.
• Step 2: Multiply $7$ by $9$. This gives $63$.
• Step 3: Multiply $b$ by $a$. This gives $ab$.
• Step 4: Multiply $b$ by $9$. This gives $9b$.

After performing these operations, the expression expands to:

$7a + 63 + ab + 9b$

Rearrange the terms in standard form for the final answer, which is:

$ab + 7a + 9b + 63$

Therefore, the solution to the problem is $ab + 7a + 9b + 63$.

Let's simplify the given expression, using the extended distribution law to open the parentheses :

$(\textcolor{red}{t}+\textcolor{blue}{b})(c+d)=\textcolor{red}{t}c+\textcolor{red}{t}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d$

Note that in the formula template for the above distribution law, we take by default that the operation between the terms inside of the parentheses is addition. Remember that the sign preceding the term is an inseparable part of it. Apply the rules of sign multiplication so that we can present any expression in parentheses. We'll open the parentheses using the above formula, as an expression where addition operation exists between all terms. In this expression it's clear, all terms have a plus sign prefix.

Therefore we'll proceed directly to opening the parentheses as shown below:

$$:

$(\textcolor{red}{a}+\textcolor{blue}{15})(5+a)\\ \textcolor{red}{a}\cdot 5+\textcolor{red}{a}\cdot a+\textcolor{blue}{15}\cdot 5 +\textcolor{blue}{15}\cdot a\\ 5a+a^2+75+15a$

In calculating the above multiplications, we used the multiplication table and the laws of exponents for multiplication between terms with identical bases:

$x^m\cdot x^n=x^{m+n}$

In the next step we'll combine like terms, which we define as terms where the variable (or variables each separately), in this case a, have identical exponents. (In the absence of one of the variables from the expression, we'll consider its exponent as zero power, this is due to the fact that any number raised to the power of zero equals 1) Apply the commutative law of addition and arrange the expression from highest to lowest power from left to right (we'll treat the free number as power of zero):
$\textcolor{purple}{5a}\textcolor{green}{+a^2}+75\textcolor{purple}{+15a}\\ \textcolor{green}{a^2}\textcolor{purple}{+5a+15a}+75\\ \textcolor{green}{a^2}\textcolor{purple}{+20a}+75\\$In the combining of like terms performed above, we highlighted the different terms using colors, and as emphasized before, we made sure that the sign preceding the term is an inseparable part of it,

We therefore got that the correct answer is answer B.

Let's simplify the expression by opening the parentheses using the distributive property:

$(\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d$

Therefore, the correct answer is (a).