# Algebra and General Mathematics: Special Products

Review notes in Special Products topic in Algebra and General Mathematics. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.

#### 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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