Algebra 1 Question

Question

Write each of the following binomial products as an equivalent polynomial written in standard form.

1) (x+3) (x+6)

2) (3x+1) (2x+7)

3) (5x-1) (x+2)

Answer 1

Hi Gilbert,

You can find the product of the given binomials using the following 2 methods:

M1) Using Distributive Property

M2) Using the FOIL Method

The standard form of a polynomial is written such that the term with the highest power comes first and is then followed by the other terms in decreasing power order of the variable.

Solution - Part 1 (Using M1) : (x+3)(x+6) = ?

(x+3)(x+6) = x(x+6) + 3(x+6) --- Distribute (x+6) to each term of (x+3)

= x(x) + x(6) + 3(x) + 3(6) --- Distributive Property

= x² + 6x + 3x + 18 --- Multiply

= x² + 9x + 18 --- Combine like terms

= x² + 9x + 18 --- Standard Form

Solution - Part 2 (using M2): (3x+1) (2x+7) = ?

The F-O-I-L stands for first, outer, inner, and last.

First - multiply the first terms together, (3x+1) (2x+7) --- 3x(2x)

Outer - multiply the outermost terms together (3x+1) (2x+7) --- 3x(7)

Inner - multiply the innermost terms together (3x+1) (2x+7) --- 1(2x)

Last  - multiply the last terms together (3x+1) (2x+7) --- 1(7)

   

(3x+1) (2x+7) = 3x(2x) + 3x(7) + 1(2x) + 1(7)

= 6x² + 21x + 2x + 7 --- Multiply

= 6x² + 23x + 7 --- Combine like terms

= 6x² + 23x + 7 --- standard Form

Solution - Part 3 (using M1):  (5x-1) (x+2) = ?

(5x-1) (x+2) = 5x(x+2) -1(x+2) --- Distribute (x+2) to each term of (5x-1)

= 5x(x) +5x(2) -1(x) -1(2) --- Distributive Property

= 5x² + 10x - x  - 2               --- Multiply

= 5x² + 9x - 2               --- Combine like terms

= 5x² + 9x - 2              --- Standard Form

Hope this helps!

Answer 2

Standard Form -> Ax²+Bx+C

Use the F.O.I.L. method of multiplication (a pneumonic to remember to distribute all your terms).

F- First

O- Outside

I- Inside

L- Last

1. (x+3)(x+6)

Multiply the first terms (x*x)=x²

Multiply the outside terms (x*6)=6x

Multiply the inside terms (3*x)=3x

Multiply the last terms (3*6)=18

Add all the products together: x² + 6x +3x + 18

Combine like terms: x² + 9x + 18

The solution to 1, in standard form is x² + 9x + 18.

Answer 3

You would typically use what is called the FOIL method to do this where the "F" in FOIL stands for "FIRST" meaning you multiply the first term in (x + 3), which is "x", with the first term in (x + 6) which is also "x". Then multiply the two OUTSIDE terms, then the two INSIDE terms, and finally, the two LAST terms. Like this:

First•First = x²

Outside•Outside = 6x

Inside•Inside = 3x

Last•Last = 18

So the polynomial becomes x² + 6x + 3x + 18 and then, combining like-terms, it becomes x² + 9x + 18

Do the other problems the same way.