Expand and simplify the expression.
Rachel's solution:
Area of square = length x length
= ( x + 5 ) 2
= x2 + 52
= x2 + 25 cm2
There is something wrong with Rachel's solution.
- Show how you would solve the problem.
- Explain the error in Rachel's solution.
( x + 5 ) ^2 = ( x + 5 ) X ( x + 5 )
ReplyDelete= x^2 + 10x + 25
using FOIL method the answer is ( x^2 + 10x + 25 )
her answer is wrong because she did not multiply x with 5 and 5 with x , instead she multiplied x with x and 5 with 5
Using the F.O.I.L method, the solution should be:
ReplyDelete(x+5)^2=(x+5)(x+5)
=x^2+5x+5x+25
=X^2+10x+25
Rachel did not multiply the brackets with each other but rather shifted the ^2 into the brackets with the x and 5 which is incorrect. The parenthesis should come before exponential order hence, the ^2 should take place on the brackets.
Rachel's solution is wrong as she didn't use the correct method to get the answer for ( x + 5 ) 2 she just square the numbers in the bracket(which is wrong)
ReplyDeleteThe correct way to solve it is by using the FOIL method -> (x + 5)^2 = (x +5)(x+5)=x^2 +10x + 25.
(x+5)^2
ReplyDelete=(x+5)(x+5)
= x^2 + 5x + 5x + 25
= x^2 + 10x + 25
Rachel thought that (x+5^2) was x^2 + 5^2 whereas the correct 'sub-step' to get the right answer is supposed to be: x(x+5) + 5(x+5)
if she were to actually write the step out. Or we could use the FOIL method, with arrows to guide her, such that we don't make careless mistakes.
(x+5)^2 does not equal to x^2+5^2 but actually equals to (x+5)(x+5) and according to the foil method it will equal to x^2+10x+25
ReplyDeleteActually I didnt realise what went wrong till I saw others' comments :p
ReplyDeleteAnyways.
She did not use the FOIL method in multiplying (x+5)^2 Which is why she got the step wrong.
This question is so easy to make mistake...like me lol.
ReplyDeleteShe simply assumed that (x+5)^2 equates to x^2 + 5^2, but that is wrong, she should have used the foil method to equate this.
Those who attempted and are able to explain the error: Well done!
ReplyDeleteGood to hear that Mervin has learnt from the rest and discovered what went wrong.
Jia En is also right to remind us not to take a seemingly easy question too lightly.
:)