Algebra and General Mathematics: Special Products

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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