Expand and simplify the expression.

*Rachel's solution:*

*Area of square = length x length*

*= ( x + 5 )*

^{2}

=

*x*

^{2}

*+ 5*

^{2}

=

*x*

^{2}

*+ 25 cm*

^{2}

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.

:)