Maths Question, Implied Multiplication Here?

[Waldo]

Expand and simplify…(6x + 7) (x + 4)

 

It seems (so I am told) there is some kind of implied multiplication of whats between each set of parentheses.

 

Argh! I am so dim, I don’t understand basic rules of mathematics; I always thought x or . implied multiplication; but what other maths terminology or conventions imply multiplication?

 

Thanks!

[Prettytom]

15 minutes ago, Waldo said:

Expand and simplify…(6x + 7) (x + 4)

 

It seems (so I am told) there is some kind of implied multiplication of whats between each set of parentheses.

 

Argh! I am so dim, I don’t understand basic rules of mathematics; I always thought x or . implied multiplication; but what other maths terminology or conventions imply multiplication?

 

Thanks!

Multiply 6x by x  = 6x squared.

Multiply 6x by 4 = 24x

Multiply x by 7 = 7x

Multiply 7 by 4 = 28

 

Add the two x terms together = 31x

 

Answer = 6x squared + 31x + 28

 

In this case the two brackets next to each other imply multiplication.😁

Edited February 5, 2023 by Prettytom

[godin]

Don't know why you're calling yourself dim. I've not thought about this before (which is dim)

I'd guess the reason we've got several ways to write multiplication is to avoid confusion between symbols:

x and ×
. and ·

By convention multiplication is implicit, and the other notations are used to avoid ambiguity.

Eg. "2πr" is equivalent to 2 times π times r, but if we use 3.14 as an approximation of π, then it would be harder to read in these notations:

2 3.14r

2·3.14r

It easy to make mistakes in those cases if the spacing isn't clear.

To make it clearer we can write something like:

2 × 3.14r

2(3.14r)

2 × 3.14 × r

Which notation you use probably depends on what area you're working in, and I think conventions have changed over time.

There are some situations where there is more than one kind or multiplication, eg cross product and dot product when working with vectors.

There are also situations where only allowing implicit multiplication and using parentheses would be confusing if it conflicted with notation to denote function.

[Padders]

Ruddy hell,

I've only just got mi head around the 2 times table.

[Bargepole23]

4 hours ago, Prettytom said:

Multiply 6x by x  = 6x squared.

Multiply 6x by 4 = 24x

Multiply x by 7 = 7x

Multiply 7 by 4 = 28

 

Add the two x terms together = 31x

 

Answer = 6x squared + 31x + 28

 

In this case the two brackets next to each other imply multiplication.😁

FOIL innit.

[Prettytom]

23 minutes ago, Bargepole23 said:

FOIL innit.

 

[Tipstaff]

Is it true that a constipated mathematician works it out with a pencil?   😁😁😆

[Waldo]

22 hours ago, Prettytom said:

Multiply 6x by x  = 6x squared.

Multiply 6x by 4 = 24x

Multiply x by 7 = 7x

Multiply 7 by 4 = 28

 

Add the two x terms together = 31x

 

Answer = 6x squared + 31x + 28

 

In this case the two brackets next to each other imply multiplication.😁

Thanks. I understand what you’ve done, so...

 

(a + b) (c + d) resolves to a*c + a*d + b*c + b*d

 

Is there a name for the convention, does it relate to matrix multiplication (though, I think they may use square brackets).

 

I’m also wondering, what if...

 

(a - b) (c - d)

 

is that meaningful within maths language.

[fools]

why are you learning algebra at your age

[Waldo]

22 hours ago, godin said:

Don't know why you're calling yourself dim. I've not thought about this before (which is dim)

I'd guess the reason we've got several ways to write multiplication is to avoid confusion between symbols:

x and ×
. and ·

By convention multiplication is implicit, and the other notations are used to avoid ambiguity.

Eg. "2πr" is equivalent to 2 times π times r, but if we use 3.14 as an approximation of π, then it would be harder to read in these notations:

2 3.14r

2·3.14r

It easy to make mistakes in those cases if the spacing isn't clear.

To make it clearer we can write something like:

2 × 3.14r

2(3.14r)

2 × 3.14 × r

Which notation you use probably depends on what area you're working in, and I think conventions have changed over time.

There are some situations where there is more than one kind or multiplication, eg cross product and dot product when working with vectors.

There are also situations where only allowing implicit multiplication and using parentheses would be confusing if it conflicted with notation to denote function.

This is brilliant, and I’ve had to read a couple of times, but it makes perfect sense. Thank you for sharing this explanation.

 

(a + b) (c + d) is the same as (a + b) * (c + d)

 

* is another symbol that represents multiply, usually within a computer code context.