# How to compute mathematical problems involving Multiplying binomial and trinomial

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To multiply a binomial by another binomial, you should multiply the two terms of the first binomial by the two terms of the second binomial using a method called foil, and then combine like terms to simplify.

Or simply use distributive property to solve it, just like on whole numbers:

(4 + 3) (3 - 4)

4 x 3 = 12

4 x -4 = -16

3 x 3 = 9

3 x -4 = -12

12 -16 +9 -12

-7

Ex.

Solve:

(4x + y)(7x - y)

+4x · +7x =

+4x · -1y =

+1y · +7x =

+1y · -1y =

(Find if the product is going to be + or -)

+4x · +7x = +

+4x · -1y = -

+1y · +7x = +

+1y · -1y = -

(Multiply the numerical coefficients by the other)

+4x · +7x = +28

+4x · -1y = -4

+1y · +7x = +7

+1y · -1y = -1

(Add the literal coefficients by the other)

+4x · +7x = +28x²

+4x · -1y = -4xy

+1y · +7x = +7xy

+1y · -1y = -1y²

(Write the equation ----------- form)

28x² - 4xy + 7xy - 1y²

(Simplify by combining like terms)

28x² + 3xy - y²

is the answer.

Same method is applied on trinomials, and multinomials.

Or simply use distributive property to solve it, just like on whole numbers:

(4 + 3) (3 - 4)

4 x 3 = 12

4 x -4 = -16

3 x 3 = 9

3 x -4 = -12

12 -16 +9 -12

-7

Ex.

Solve:

(4x + y)(7x - y)

+4x · +7x =

+4x · -1y =

+1y · +7x =

+1y · -1y =

(Find if the product is going to be + or -)

+4x · +7x = +

+4x · -1y = -

+1y · +7x = +

+1y · -1y = -

(Multiply the numerical coefficients by the other)

+4x · +7x = +28

+4x · -1y = -4

+1y · +7x = +7

+1y · -1y = -1

(Add the literal coefficients by the other)

+4x · +7x = +28x²

+4x · -1y = -4xy

+1y · +7x = +7xy

+1y · -1y = -1y²

(Write the equation ----------- form)

28x² - 4xy + 7xy - 1y²

(Simplify by combining like terms)

28x² + 3xy - y²

is the answer.

Same method is applied on trinomials, and multinomials.