5 Form Factoring Formulas In Algebra

Factoring In Algebra is to declare the sum form into a multiplication of the algebraic form. A numbered operation that has been factored will be easier to operate.

Here are 5 Form Factoring Formulas In Algebra:

1. ax + ay + az + ... and ax + bx - cx form
An algebraic form consisting of two or more tribes and having allied factors can be factored by using distributive properties:
ax + ay + az + ... = a(x + y + z + ...)
ax + bx - cx = x(a + b - c)

Example:
Please factoring 2x + 2y !!!

Answer:
2x + 2y Have ally factor 2, so:
2x + 2y = 2(x + y)

So the factor of 2x + 2y is 2(x + y)

2. The difference form of two squares x² - y²

The algebraic form consisting of two tribes and is the quadratic difference can be factored by:
x² - y² = (x + y)(x - y)

Example:
Please factoring 9x² - 25y² !!!

Answer:
9x² - 25y² = (3x)² - (5y)²
9x² - 25y² = (3x + 5y)(3x - 5y)

So the factor of 9x² - 25y² is (3x + 5y)(3x - 5y).

3.  x² + 2xy + y² and x² - 2xy + y² form

To factize the algebraic form x² + 2xy + y² and x² - 2xy + y² can be done in the following way:
x² + 2xy + y² = (x + y)(x + y) = (x + y)²
x² - 2xy + y² = (x - y)(x - y) = (x - y)²

Example:
Please factoring x² - 4x + 4 !!

Answer:
x² - 4x + 4 = x² - 2(2x) + 2²
x² - 4x + 4 = (x - 2) (x - 2)
x² - 4x + 4 = (x - 2)²

So the factor of x² - 4x + 4 is (x - 2)²

4. ax² + bx + c form, with a = 1
To fact form ax² + bx + c can be done by searching for two real numbers whose product is equal to c and the number is equal to b. :
x² + bx + c = (x + m)(x + n) with m x n = c and m + n = b

Example :
Please factoring x² + 4x + 3 !!!!!

Answer:
a = 1
b = 4
c = 3
m x n = c
m x n = 3
m + n = b
m + n = 4

Then:
m = 1
n = 3
x² + bx + c = (x + m) (x + n)
x² + 4x + 3 = (x + 1) (x + 3)

So the factor of x² + 4x + 3 is (x + 1) (x + 3).

5. ax² + bx + c form, with a ≠ 1, a ≠ 0
To fact ax²  + bx + c with a ≠ 1, a ≠ 0 can be done by:
ax² + bx + c = 1/a (ax + m) (ax + n) with m x n = a x c and m + n = b

Example:
Determine the factor of 3x² + 14x + 15 !!

Answer:
a = 3
b = 14
c = 15

m x n = a x c
m x n = 3 x 15
m x n = 45
m + n = b
m + n = 14

So:
m = 9
n = 5
3x² + 14x + 15 = 1/3 (3x + 9) (3x + 5)
3x² + 14x + 15 = (1/3) 3(x + 3) (3x + 5)
3x² + 14x + 15 = (x + 3) (3x + 5)

So the factor of 3x² + 14x + 15 is (x + 3) (3x + 5).

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Reference:

• Matematikaakuntansi.blogspot.com

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