Solve 8a-b(7+a) with a=50 and b=0: Algebraic Expression Evaluation

Algebraic Substitution with Zero Values

What will be the result of this algebraic expression:

8ab(7+a) 8a-b(7+a)

if we ascertain that:

a=50,b=0 a=50,b=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Set up and solve
00:04 Let's substitute appropriate values according to the given data and solve
00:13 Let's calculate the multiplication
00:19 Always solve parentheses first
00:24 0 multiplied by any number always equals 0
00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What will be the result of this algebraic expression:

8ab(7+a) 8a-b(7+a)

if we ascertain that:

a=50,b=0 a=50,b=0

2

Step-by-step solution

Let's insert the given data into the expression:

8*50-0(7+50) =
400-0*57 =
400-0 =
400

3

Final Answer

400 400

Key Points to Remember

Essential concepts to master this topic
  • Substitution Rule: Replace variables with their exact given values first
  • Technique: When b=0, the term b(7+a) becomes 0×57 = 0
  • Check: Substitute back: 8(50) - 0(7+50) = 400 - 0 = 400 ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the zero multiplier
    Don't calculate (7+a) when b=0 and worry about the parentheses = wasted time and confusion! When any factor is zero, the entire product equals zero regardless of what's in parentheses. Always recognize that b(7+a) = 0×(anything) = 0 when b=0.

Practice Quiz

Test your knowledge with interactive questions

What will be the result of this algebraic expression:

\( 5x-6 \)

if we place

\( x=8 \)

FAQ

Everything you need to know about this question

Why does b(7+a) equal zero even though (7+a) = 57?

+

Great question! When any factor in multiplication is zero, the entire product is zero. So b(7+a) = 0×57 = 0. It doesn't matter what's inside the parentheses!

Do I still need to calculate what's in the parentheses?

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Technically no, but it's good practice! Calculating (7+50) = 57 helps you understand the expression structure, even though 0 times anything equals 0.

What if both a and b were zero?

+

If a=0 and b=0, then 8ab(7+a) 8a-b(7+a) becomes 8(0)0(7+0)=00=0 8(0)-0(7+0) = 0-0 = 0 . Zero values make calculations much simpler!

How do I avoid calculation mistakes with substitution?

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Follow these steps:

  • Write out the original expression
  • Substitute each variable with its value
  • Simplify step by step
  • Double-check by substituting your answer back

Is there a faster way to solve this type of problem?

+

Yes! When you see any variable equals zero, look for terms containing that variable. Those entire terms will equal zero, making the problem much simpler to solve.

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