### Chapter 5: Algebra - Can you tell where has gone wrong?

Textbook (p89)

Julie says that
3a² + 2a + 5a² = 10a³
and
7b x 5b² x 6 = 210b
Do you agree with Julie? If not, what are the mistakes in her algebraic manipulations?

Complete this for Monday's (25 April) discussion

1. I do not agree as Julie has calculated the numbers or expressions without multiplying them by their power first. And plus the end product does not even include the power or has an incorrect one.

2. I do not agree as Julie will have to multiply the numbers by the power first before solving the question step by step but instead of doing that she just do it with only 1 steps

3. I do not agree, for both.

1st one. Example. If a=2, 3x2x2+2x3+5x2x2=10x2x2x2
12+6+20=80
40=80
Which is wrong, she regarded the '+' into 'x' which is times.

2nd one. Eg.b=2, (7x2)x(5x2x2)x6=210x2
14x20x6=420
1680=420
Which is wrong. She thought 5b^2x6 = 5bx6b but this is wrong.

4. I do not agree with Julia. For 3a² + 2a + 5a² = 10a³, 3a^2 is equal to 3a * 3a but Julia just simply added the constant without looking at the ^.
For 7b x 5b² x 6 = 210b, to get the constant which is 210, she multiplied 7*5*6 , but for 5b^2 it should be 5b*5b.

5. I do not agree with Julia.3a^2=3*(a*a)=(a*a)+(a*a)+(a*a)=6a.5a^2=5*(a*a)=(a*a)+(a*a)+(a*a)+(a*a)+(a*a)+10a.Therefore, 3a^2+2a+5a^2=6a+2a+10a=18a.10a^3=10*(a*a*a)=(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)+(a*a*a)=30a.18a does not=30a.

I do not agree with Julia.5b^2=5*(b*b)=(b*b)+(b*b)+(b*b)+(b*b)+(b*b)=10b.17b*6=102b which is not=210b.

6. I do not agree with Julie.

1. 3a² + 2a + 5a² = 10a³

The terms with the variables a^2 and a is to be worked differently but not together. She should only be adding the terms with the variables , a^2 together . She should not be adding the coefficients together. The answer is presented in a^3 but there is no multiply sign in the equation to multiple 'a^2 and 'a' to derived a answer - a^3.

I think the answer should be

3a² + 2a + 5a² = 3a^2+ 5a^2 + 2a
= 8a^2 + 2a

2. 7b x 5b² x 6 = 210b

She presented her answer with a variable - 'b'. There is multiply signs between the terms '7b' and '5b^2' so she should be multiplying the coefficients together and adding the exponents together.

7b x 5b^2 = 35b^3

After the multiplication of the two terms , multiple 35b^3 by 6.

35b^3 X 6 = 210 b^3 The answer should be 210b^3 not 210b.

7. I do not agree as Julie will have to multiply the numbers by the power first before solving the question step by step but instead of doing that she just do it with only 1 step, thus it is wrong

8. Mark :) :( :&#39;( (^^^) :D :O :42: O:) :p 3:)4/23/2011 11:29:00 AM

I do not agree with Julia.

1) Where she said 3a² + 2a + 5a² = 10a³, she took the + sign in 3a² + 2a as a multiplication, therefore making the variable "³", and then added the 5a² wrongly, giving an answer that is completely wrong.

2) Where she said 7b x 5b² x 6 = 210b, she forgot to calculate in the equation the "b²" of "5b²", therefore giving the answer 210b.

9. I do not agree with Julia. She calculated the expression by just adding or multiplying the coefficients

10. I do not agree with Julie. She only added/multiplied the coefficients and did not take notice of the powers.

11. I don't agree with Julie as she did not count the powers (^) and only added and multiplied the expression .

12. No, I do not agree with Julie. a and a^2 are different, thus they cannot be added together and it cannot get a^3. The correct answer is 8a^2 + 2a.

b x b^2 is not b. The correct answer is 210b^3.

13. I do not agree with Julie.

For the 1st equation,she just simply see how many 'a's in the equation and put it as the powers,instead of calculating the powers.

For the 2nd equation,she neglected the powers of the equation and simply multiplied the numbers.

14. Its just wrong...ALL WRONG
Obviously I don't agree with her...

Firstly:
a^2 is a different term compared to a itself thus you cannot add their coefficients together just like what you do when there are like terms.Because a^2≠a

3a² + 2a + 5a²
=3aa+2a+5aa
=a(3a+2+5a)
=a(8a+2)
=8a^2+2a

8a^2+2a≠10a^3

Secondly:
As for this case,her coefficient is correctly multiplied together,but she forgot to multiply b^2 and b together...

7b x 5b² x 6
=7*5*6*b*b^2
=210*b^3
=210b^3

15. I do not agree with her.

First:
3a² + 2a + 5a²
=(3 x a x a) +(2 x a)+5 x a x a)
=a(3a + 2+ 5a)
=a(8a + 2)
=8a²+2a

a² is (a x a) while 2a = (2 x a) these two are different.

Second:
7b x 5b² x 6
= (7 x b) x (5 x b x b) x 6
= b(7 x 5b x 6)
= b(210b)
= 210b²

This is so as (210b x b)
= (210 x b x b)
= 210b²

16. I do not agree with Julie
1.She did not notice the powers of "a" and simply add the number of times "a" appeared

2.She just calculate the numbers first then just added the b at the back

17. I do not agree with Julie. she just added the numerical values and then number of 'a's together without adding in the notations. For the second one, she blindly multiplied the numbers then without calculating the correct value of the 'b's, she just added a single 'b'.

18. I do not agree with Julie.

a² is different from a thus you cannot group a² and a together into one term. She did not notice the powers and only did the multiplication.