distributivity when developing a polynomial

[cmatlack]

Hello,
I have the following which needs to be developed...
-7(a-9)(8-5a)
I am not sure how distributivity applies here, do I multiply -7 times (a-9) and then multiply the result of that by (8-5a)? in other words -7a + 63 multiplied by 8 - 5a?
thank you.

 

[stapel]

I have the following which needs to be developed...
-7(a-9)(8-5a)

I've never heard of "developing" a polynomial. I'll guess that means what is usually called "expanding".

I am not sure how distributivity applies here....

Multiplication "distributes over" addition (and subtraction). Since you're multiplying something on a subtraction (namely, 8 - 5a), you have to "distribute".

. . . . .(a - 9)(8 - 5a) = (a - 9)(8) + (a - 9)(-5a)

Now, of course, you have to distribute through the other subtraction, the a - 9:

. . . . .(a)(8) + (-9)(8) + (a)(-5a) + (-9)(-5a)

When you're done with that, you'll need to distribute the -7.

 

[cmatlack]

Thank you (and sorry for the confusion, the course is actually in French, and they use the word "develop" for "expand.")
Just to be sure I am clear on this, when I expand (a-9) (8-5a) I get 8a - 5a squared - 72 +45a, which simplifies to 5a squared + 53a - 72.
So then after that....I distribute - 7 over (5a squared + 53a - 72) which would be 35a squared - 371a + 504. Is that right?

 

[stapel]

You got it!