### 6AM Quiz (20110730) What's Wrong with the Area of Square Sticker

Write down the expression for the area of the square (not drawn to scale) shown.
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.

1. ( x + 5 ) ^2 = ( x + 5 ) X ( x + 5 )
= 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

2. Using the F.O.I.L method, the solution should be:
(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.

3. 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)

The correct way to solve it is by using the FOIL method -> (x + 5)^2 = (x +5)(x+5)=x^2 +10x + 25.

4. (x+5)^2
=(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.

5. (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

6. Actually I didnt realise what went wrong till I saw others' comments :p
Anyways.
She did not use the FOIL method in multiplying (x+5)^2 Which is why she got the step wrong.

7. This question is so easy to make mistake...like me lol.

She 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.

8. Those who attempted and are able to explain the error: Well done!
Good 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.

:)