Solve the Equation: 32(? + ?) = 8 + 2a - Finding Missing Values

Fill in the missing values:

32(?+?)=8+2a 32(?+?)=8+2a

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Complete the missing values
00:04 Multiply by the appropriate whole fraction
00:21 Raise the products to the numerator
00:25 Factor 32 into factors 8 and 4
00:32 Factor 32 into factors 16 and 2
00:35 Reduce what is possible
00:49 Mark the common factors
00:52 Take out the common factors from the parentheses
01:02 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Fill in the missing values:

32(?+?)=8+2a 32(?+?)=8+2a

2

Step-by-step solution

To solve the equation 32(?+?)=8+2a 32(?+?)=8+2a , follow these steps:

  • First, observe the equation: 32(?+?)=8+2a 32(? + ?) = 8 + 2a .
  • Factor out 32 32 on the left side: it should already involve distribution.
  • On the right side, we see 8+2a 8 + 2a can potentially be related to 32 32 : 8=14⋅32 8 = \frac{1}{4} \cdot 32 and 2a=116a⋅32 2a = \frac{1}{16}a \cdot 32 .
  • Therefore, express the equation as:
32(14+116a)=8+2a 32\left(\frac{1}{4} + \frac{1}{16}a\right) = 8 + 2a

This demonstrates that the missing values to satisfy the equation's balance, by distribution properties, are:

14 and 116a \frac{1}{4} \text{ and } \frac{1}{16}a

Thus, the completed form of the right side of the equation with respect to 32 32 is:

Hence, the solution is: 14,116a \frac{1}{4}, \frac{1}{16}a .

3

Final Answer

14,116a \frac{1}{4},\frac{1}{16}a

Practice Quiz

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Break down the expression into basic terms:

\( 4x^2 + 6x \)

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