Julie says that

**3**

*a*² + 2*a*+ 5*a*² = 10*a*³and

**7**

*b*x 5*b*² x 6 = 210*b*Do you agree with Julie? If not, what are the mistakes in her algebraic manipulations?

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No. For 3a² + 2a + 5a² ≠ 10a^3

ReplyDeleteit 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

a² + 2a + 5a²=(3*a*a)+(2*a)+(5*a*a*a)

ReplyDelete≠(10a³)

10a³=(3+2+5)*a*a*a

7b*5b²*6=(7*b)*(5*b*b)*6

≠210b

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

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ReplyDeleteNo 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).

ReplyDeleteNO.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.

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

ReplyDelete7b x 5b² x 6 = 210b^3

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

ReplyDeleteWhy?

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)