Questions on Algebra: Operations with Signed Numbers answered by real tutors!

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Question 109894: I have a problem I would like to get your opinion on for my answer.
Here it is: Evaluate each of the expressions if a=-2, b=5, c=-4, d=6 So here is the problem: b(with a sq rt of 2) - 2bc + c (with a sq. rt of 2)
My answer is this 5(5)- 2(5)(-4)+(-4 sq. rt of 2) am I on the right track here for my answer.
I am sorry I could not place the sq.rt of 2 with the first letter "b" and the last letter "c" I could not figure out on this web page how to do that. I appreciate your help on this for me.
Thank you, Barb Neely: I have a problem I would like to get your opinion on for my answer.
Here it is: Evaluate each of the expressions if a=-2, b=5, c=-4, d=6 So here is the problem: b(with a sq rt of 2) - 2bc + c (with a sq. rt of 2)
My answer is this 5(5)- 2(5)(-4)+(-4 sq. rt of 2) am I on the right track here for my answer.
I am sorry I could not place the sq.rt of 2 with the first letter "b" and the last letter "c" I could not figure out on this web page how to do that. I appreciate your help on this for me.
Thank you, Barb Neely
Answer by JessicaGill(39) About Me  (Show Source):
You can put this solution on YOUR website!
b^2-2bc+c^2
With b=5 and c=-4 the substitution will look as follows
5^2-2*5*-4+-4^2
Per the order of operations we need to process the exponents first
5^2 becomes 25 and -4^2 becomes 16
Replace in the equation
25-2*5*-4+16
Next simplify any multiplication. 2*5*-4 becomes -40
Replace in the equation
25-(-40)+16 Note that there are 2 minus signs with the 40. This will convert the negative 40 into a positive 40, thus the equation will look like this in its finality 25+40+16
Simplify
Your answer should be 81
I have applied the universal simplifier and solver as well so that you can see the steps in animation. Also, if you want to show a number raised to a power of another number use the carat symbol (shift and the number 6 (^) on your keyboard.) Just a helpful hint.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:
Simplify 5^2-2*5*-4+4^2
  • Graphical form: 5^2-2*5*-4+4^2 simplifies to 81
  • Text form: 5^2-2*5*-4+4^2 simplifies to 81
  • Cartoon (animation) form: simplify_cartoon( 5^2-2*5*-4+4^2 )
    simplify_cartoon( 5^2-2*5*-4+4^2 )

Detailed explanation:

Look at highlight_red( 5 )^highlight_red( 2 )-2*5*-4+4^2.
Replace constants in factor: highlight_red( 5 ),highlight_red( 2 ) with highlight_green( 25 )
It becomes highlight_green( 25 )-2*5*-4+4^2.
Look at 25-highlight_red( 2 )*highlight_red( 5 )*highlight_red( -4 )+4^2.
Multiplied numerator integers
It becomes 25-highlight_green( -40 )+4^2.
Look at 25--40+highlight_red( 4 )^highlight_red( 2 ).
Replace constants in factor: highlight_red( 4 ),highlight_red( 2 ) with highlight_green( 16 )
It becomes 25--40+highlight_green( 16 ).
Look at highlight_red( 25 )-highlight_red( -40 )+highlight_red( 16 ).
Added fractions or integers together
It becomes highlight_green( 81 ).
Result: 81

Done!