How do you evaluate this? (x + 7)(x2 – 3x + 2). Please, step by step solving, so I can understand.

Answer 1

To help understand this problem, let's try one that doesn't have any variables. If I asked you, what is

(1 + 7) * (1 - 3 + 2)?

You could solve this a few ways. You would probably simply inside of the parentheses to give you (8)*(0) which = 0. That's the quickest way.

Another correct way to solve would be to multiply by grouping. We could split up the 1 + 7 by distributing the 1 by multiplying it to each number in the second set of parentheses and distribute the 7 by multiplying it to each number in the second set of parentheses, so

( 1 + 7 ) * ( 1 - 3 + 2 ) would become

= [1 * ( 1 - 3 + 2)] + [7 * (1 - 3 + 2)]

= [1 * (0)] + [7 * (0)]

= 0 + 0

= 0

This is the approach we take when multiplying polynomials, like the one in your question.

Let's start by splitting up (x + 7) and distributing it so that

(x + 7)(x² - 3x + 2) becomes

[ x * (x² - 3x + 2)] + [ 7 * (x² - 3x + 2)]

We multiply the x by each term in the first set of parenthesis and we multiply the 7 by each term in the second set of parenthesis, giving us

[ ( x * x² ) + ( x * -3x ) + ( x * 2 )] + [ ( 7 * x² ) + ( 7 * -3x ) + ( 7 * 2 )]

[ x³ - 3x² + 2x] + [ 7x² - 21x + 14]

If it makes things easier, we can rearrange the expression to group like terms. Like terms are terms have the same variable letter and same exponent value,

x³ - 3x² + 2x + 7x² - 21x + 14

x³ + (- 3x² + 7x²) + (2x + - 21x) + 14

Now, we can simplify, giving us:

x³ + 4x² - 19x + 14

Answer 2

(x + 7) * (x² - 3x + 2)

using the distributive property, we have:

= x * (x² - 3x + 2) + 7 * (x² - 3x + 2)

using the distributive property again, we have:

= x³ -3x² + 2x + 7x² - 21x + 14

combining like terms:

= x³ -3x² +7x² +2x - 21x + 14

= x³ + 4x² +2x - 19x + 14