4 Special Properties Multiplication Algebraic Form

Algebra is one part of a wide field of mathematics, together with number theory, geometry and analysis. In the most general form, algebra is the study of mathematical symbols and rules for manipulating symbols. Algebra is a unifying thread of almost all areas of mathematics.

This time I share my knowledge about the special 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 and d = b
Multiplication (a - b)(c - d) for c = a and d = b
Multiplication (a + b)(c ∓ d)for c = a and d = b

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

There are two special 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 + 15 = x² + 8x + 15
(x - 3)(x - 5) = x² - (3 + 5)x + 15 = x² - 8x + 15

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

There is only one special property for multiplication (a + b) (c + d) for c = a and 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 and d = b

There is only one special property for multiplication (a - b) (c - d) for c = a and 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 and d = b

There is only one special property for multiplication (a + b) (c ∓ d) for c = a and 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 there is a wrong word.

Finally I said wassalamualaikum wr. wb.

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