# Algebra and General Mathematics: Special Products

(Last Updated On: February 5, 2020)

#### SPECIAL PRODUCTS

1. Product of Two Similar Binomials

(x + a) (x + b) = x2 + (a + b) x + ab

(ax + b) (cx + d) = acx2 + (bc + ad) x + bd

2. Product of the Sum and Difference of Two Numbers

(x + y) (x – y) = x2 – y2

3. Square of a Binomial

(x + y)2 = x2 + 2xy + y2

(x + y)2 = x2 + 2xy + y2

4. Square of a Trinomial

(x + y + z)2 = x2 + y2 + z2 + 2 (xy + xz + yz)

5. Square of a Polynomial

(a + b + c + …)2 = a2 + b2 + c2 + … + 2a (b + c + …) + 2b (c + …) + 2c (…)

6. Cube of a Binomial

(x + y)3 = x3 + 3x2y + 3xy2 + y3

(x – y)3 = x3 – 3x2y + 3xy2 – y3

7. Other Products:

(x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4

(x – y)4 = x4 – 4x3y + 6x2y2 – 4xy3 + y4

(x + y)5 = x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5

(x – y)5 = x5 – 5x4y + 10x3y2 – 10x2y3 + 5xy4 – y5

(x + y)6 = x6 + 6x5y + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6

(x – y)6 = x6 – 6x5y + 15x4y2 – 20x3y3 + 15x2y4 – 6xy5 + y6

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