4 Particular Properties Multiplication Algebraic Form

Algebra is 1 business office of a broad plain of mathematics, together alongside publish theory, geometry too analysis. In the most full general form, algebra is the written report of mathematical symbols too rules for manipulating symbols. Algebra is a unifying thread of almost all areas of mathematics.

This fourth dimension I portion my noesis near the particular properties of multiplication for algebraic forms. Here are the properties:

Multiplication (a + b)(c + d) for c = a
Multiplication (a + b)(c + d) for c = a too d = b
Multiplication (a - b)(c - d) for c = a too d = b
Multiplication (a + b)(c ∓ d)for c = a too d = b

1. Multiplication (a + b)(c + d) for c = a

There are 2 particular properties for multiplication (a + b)(c + d) for c = a, including:

(a + b)(c + d) → (a + b) (a + d) = a² + (b + d)a + bd
(a + b)(c + d) → (a - b) (a - d) = a² - (b + d)a + bd

Example:
(x + 3)(x + 5) = x² + (3 + 5)x + xv = x² + 8x + 15
(x - 3)(x - 5) = x² - (3 + 5)x + xv = x² - 8x + 15

2. Multiplication (a + b)(c + d) for c = a too d = b

There is exclusively 1 particular belongings for multiplication (a + b) (c + d) for c = a too d = b, ie:

(a + b)(c + d) → (a + b) (a + b) = (a + b)² = a² + 2ab + b²

Example:
(x + 3)(x + 3) = (x + 3)² = (x)² + 2(x)(3) + (3)² = x² + 6x + 9

3. Multiplication (a - b)(c - d) for c = a too d = b

There is exclusively 1 particular belongings for multiplication (a - b) (c - d) for c = a too d = b, ie:
(a - b)(c - d) → (a - b) (a - b) = (a - b)² = a² - 2ab + b²

Example:
(x - 3)(x - 3) = (x - 3)² = (x)² - 2(x)(3) + (3)² = x² - 6x + 9

4. Multiplication (a + b)(c ∓ d) for c = a too d = b

There is exclusively 1 particular belongings for multiplication (a + b) (c ∓ d) for c = a too d = b, ie:
(a + b)(c ∓ d) → (a + b)(a ∓ b) = a² - b²

Example:
(x + 3)(x - 3) = x² - 3² = x² - 9

End for this articles. Sorry if at that spot is a incorrect word.

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Reference:

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