(3x+6)(2x^2+7x+2)

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kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

To simplify `(3x+6)(2x^2+7x+2)`


Multiply each term in the first polynomial by each term in the second polynomial.

`(3x * 2x^2 + 3x * 7z + 3x * 2 + 6 * 2x^2 + 6 * 7x + 6 * 2)`

Multiply each term in the first polynomial by each term in the second polynomial.

`(6x^3 + 33x^2 + 48x + 12)`


Remove the parentheses around the expression `(6x^3 + 33x^2 + 48x + 12)`

Thus, the answer will be


`6x^3 + 33x^2 + 48x + 12`  

ncchemist's profile pic

ncchemist | eNotes Employee

Posted on

You do not specify but I am assuming that you want the two polynomials multiplied and then simplified.  Multiplying polynomials is easy; you just have to keep track of each term that you multiply.  In this case, you would multiply each term in (2x^2+7x+2) first by 3x and then by 6 and then algebraically sum all the terms together.

(3x+6)(2x^2+7x+2)

6x^3+21x^2+6x+12x^2+42x+12

Now add the like terms together and simplify.

6x^3+(21x^2+12x^2)+(6x+42x)+12

6x^3+33x^2+48x+12

Notice that 3 is a common factor in each coefficient above.  We can factor out the 3 for the simplest form.

3(2x^3+11x^2+16x+4)

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`(3x+6)(2x^2+7x+2)`  distribute the first parenthesis to the second

you will end up with

`6x^3+21x^2+6x+12x^2+42x+12 `

combine the like terms

`6x^3+33x^2+48x+12 `

so the answer is

`6x^3+33x^2+48x+12  `

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