Combine Like Terms 4(4a+5)
The provided expression, 4(4a+5), involves a linear term in 'a' multiplied by a coefficient and a constant term within parentheses and being multiplied by 4. The task of combining like terms here would involve distributing the multiplication of 4 into the parentheses to both the linear term '4a' and the constant term '5', then combining any like terms if applicable. This is an algebraic simplification process that aims to simplify the expression into a more compact form with as few terms as possible.
$4 \left(\right. 4 a + 5 \left.\right)$
Answer
Solution:
Step 1:
Use the distributive property to expand the expression. $4 \times (4a) + 4 \times 5$
Step 2:
Perform the multiplication.
Step 2.1:
Multiply $4$ with $4a$. This gives us $16a + 4 \times 5$
Step 2.2:
Now multiply $4$ with $5$. The result is $16a + 20$. Thus, the expression simplifies to $16a + 20$.
Knowledge Notes:
The problem is asking to simplify the algebraic expression by combining like terms. The process involves using the distributive property and multiplication of terms.
Relevant knowledge points include:
Distributive Property: This property states that for any real numbers $a$, $b$, and $c$, the equation $a(b + c) = ab + ac$ holds true. It allows us to multiply a single term by each term inside a parenthesis.
Multiplication of Algebraic Terms: When multiplying algebraic terms, we multiply the coefficients (numerical parts) and add the exponents of like bases.
Combining Like Terms: Like terms are terms that have the same variable raised to the same power. Only the coefficients of like terms are added or subtracted.
In the given problem, the expression $4(4a+5)$ is simplified by applying the distributive property to multiply $4$ by each term inside the parentheses, resulting in two terms, $16a$ and $20$, which are then written as a sum. Since there are no like terms to combine further, the expression is already simplified.
