trinomial question

[dcunited11]

ok, here is the question. and there isn't an example of this anywhere in my book!

(Find each of the following products)
(r-3s+t)(2r-s+t)


and also: (Factor each of the following polynomials by grouping)
15-5m^2-5m^2-3r^2+m^2r^2

 

[tkhunny]

ok, here is the question. and there isn't an example of this anywhere in my book!

(Find each of the following products)
(r-3s+t)(2r-s+t)

Remember FOIL? That's a trick for multiplyign BInomials. You must generalize the idea. Match EACH term in the first expression with EVERY term in the second expression.

(r-3s+t)(2r-s+t)

r*(2r)
r*(-s)
r*(t)
-3s*(2r)
-3s*(-s)
-3s*(t)
t*(2r)
t*(-s)
t*(t)

Add them all up.

 

[soroban]

Hello, dcunited11!

I assume there is a typo in the second problem . . .

Find the product: (r - 3s + t)(2r - s + t)

Take each term in the first polynomial and "distribute" it over the second polynomial.

We have: .(r - 3s + t)(2r - s + t)

Then: . r(2r - s + t) - 3s(2r - s + t) + t(2r - s + t)

Simplify: . 2r² - rs + rt - 6rs + 3s² - 3st + 2rt - st + t²

. . . . . .= .2r² - 7rs + 3rt + 3s² - 4st + t²

Factor by grouping: 15 - 5m² - 3r² + m²r²

Factor them "in pairs": . 5(3 - m²) - r²(3 - m²)

We have two groups; they have a common factor, (3 - m²).

. . Factor it out: .(3 - m²) (5 - r²)