Then, $(4x^2+3x)(4x) =$
Answer (2)
Distribute 4 x to both terms inside the parenthesis.
Multiply 4 x by 4 x 2 to get 16 x 3 .
Multiply 4 x by 3 x to get 12 x 2 .
Combine the terms to get the final answer: 16 x 3 + 12 x 2 .
Explanation
Understanding the Expression We are given the expression ( 4 x 2 + 3 x ) ( 4 x ) and we want to simplify it. This involves distributing the term 4 x to both terms inside the parenthesis.
Performing the Multiplication We need to multiply 4 x by both 4 x 2 and 3 x . Let's do this step by step:
First, multiply 4 x by 4 x 2 :
( 4 x ) ( 4 x 2 ) = 4 ⋅ 4 ⋅ x ⋅ x 2 = 16 x 3
Next, multiply 4 x by 3 x :
( 4 x ) ( 3 x ) = 4 ⋅ 3 ⋅ x ⋅ x = 12 x 2
Combining the Terms Now, we add the two resulting terms together: 16 x 3 + 12 x 2
Final Answer Therefore, the simplified expression is 16 x 3 + 12 x 2 .
Examples
Understanding how to simplify expressions like this is fundamental in algebra. For example, if you're calculating the volume of a rectangular prism where the dimensions are given in terms of x , you might end up with an expression like this. Suppose the length is 4 x , the width is x , and the height is 3 x + x 2 . The volume would be 4 x ⋅ x ⋅ ( 3 x + x 2 ) = 4 x 2 ( 3 x + x 2 ) = 12 x 3 + 4 x 4 . Simplifying such expressions helps in solving for unknown values or optimizing designs in engineering and architecture.
To simplify ( 4 x 2 + 3 x ) ( 4 x ) , we distribute 4 x to each term inside the parentheses, resulting in 16 x 3 + 12 x 2 . The final answer is 16 x 3 + 12 x 2 . Understanding this process is fundamental in algebra.
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