Question

1. Express the product of 2x2 + 7x – 10 and x + 5 in standard form.

Answer 1

Answer:

Step-by-step explanation:

It will be easier if you bring that binomial in-front, imo. But the main thing you want to do here is actually really easy. You have to distribute that x to every single term in the trinomial, then do the same thing for the 5. Add up everything.

Distribute the x and 5 like this:

$x(2x^2+7x-10) + 5(2x^2+7x-10)$

$2x^3+7x^2-10x+10x^2+35x-50$

Now combine like terms:

$2x^3+17x^2+25x-50$

There's your answer. Btw, standard form means the exponents are in order high to low and all variables before constants

Answer 2

Step 1: Start with the following:
(a + b + c)(d + e)

Step 2: Distribute (d + e) to each of the term in the first parenthesis
a(d + e) + b(d + e) + c(d + e)

Step 3: Distribute d and e to each term:
(ad + ae) + (bd + be) + (cd + ce)
or ad + ae + bd + be + cd + ce without the parentheses.

Step 4: Finally, simplify.