## Sunday, May 1, 2011

### Chapter 4: 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?

Note: to enter superscripts, you may use the code
• & sup 2 ; (type them without space) to raise to the power of 2
• & sup 3 ; (type them without space) to raise to the power of 3

1. No. For 3a² + 2a + 5a² ≠ 10a^3
it is because that a^2 is variable and a is another variable. so the ans would be 8a^2 + 2a.while for 7b x 5b² x 6 ≠ 210b because b x b² = bxbxb so it would be b^3 so,7b x 5b² x 6 = 210b^3

2. a² + 2a + 5a²=(3*a*a)+(2*a)+(5*a*a*a)
≠(10a³)

10a³=(3+2+5)*a*a*a

7b*5b²*6=(7*b)*(5*b*b)*6
≠210b

210b=(5*6*7)*b

3. This comment has been removed by the author.

4. No for both equations. a² is a variable and a is also a variable. So it cannot be put together as 10a³. The same can be said for 7b and 5b². b is a variable and b² is another variable so they cannot be put together as Julie has done (210b).

5. NO.a^x and b^y is different to a, b or a^y and b^x. a^2 + a will not give the answer of a^3 as it is an addition not a multiplication. b^2 x b = b^3 as this is a multiplication.

6. No, 3a² + 2a + 5a² = 8a^2 + 2a

7b x 5b² x 6 = 210b^3

7. Statement 1 : 3a² + 2a + 5a² = 10a³ , Statement is wrong.

Why?

3a² + 2a + 5a² = 8a² + 2a

To achieve 10a³, the statement would need to be :

2a x a x 5a = 10a³.

Let's bring it back to the basics, whole numbers (Integers).

Lets take a = 3

3a² + 2a + 5a²
= 3x3² + 2x3 + 5x3²
= 27 + 6 + 45
= 33 + 45
= 78

As what Julie claims, the final answer would be 10a³

10a³ would be equal to -> 10x3³ = 10x27 = 270

3a² + 2a + 5a² ≠ 10a³
(78 if a = 3) (270 if a =3)

Statement 2 : 7b x 5b² x 6 = 210b, Statement is wrong.

Why?

7b x 5b² x 6 = (7 x 5) x (b x b²) x 6 = 35 x b³ x 6 = 35b³ x 6 = 210b³

Lets take b as 2.

7b x 5b² x 6 = (7 x 2) x (5 x 2²) x 6 = 14 x 20 x 6 = 280 x 6 = 16x80

210b = 210x2 = 240

7b x 5b x 6 ≠ 210b
(1680 if b = 2) (240 if b = 2)