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.
