Easy pre algebra help
Introduction :
Let us learn a easy way of pre algebra help. Easy Pre algebra is a common name for a course in middle school mathematics. easy Pre-algebra often includes some basic subject from geometry, mostly the kinds that further understanding of algebra and show how it is used, such as area, volume, and perimeter. easy included New types of numbers such as integers, fractions, decimals and negative numbers and Simple (integer) roots and powers.(Source.Wikipedia)
Easy pre algebra Special products help:
Let us consider three special product which occur very frequently in algebra They are :
(i) (a+b)2 =a2+2ab+b2
(ii) (a-b)2 =a2 -2ab +b2
(iii) (a+b)(a+b)=a2+b2
Examples:
(i) (5+ 2)2 = 52 + (2 *5 *2) + 22 or 49 = 49 or 72
(ii) (5− 2)2 = 52 − (2 *5* 2) + 22 or9 = 9 or 32
(iii) (5+ 2)(5− 2) = 52 − 22 or21 = 21
Example 1 :
Evaluate(a) (2x + 3y)2 (b) (x2 + 2y2 )(x2 − 2y2 )
(a) (2x + 3y)2 = (2x)2 + 2 ( 2x 3y )+ (3y)2
= 4x2 +12xy + 9y2
(b) (x2 + 2y2 )(x2 − 2y2 ) = (x2 )2 − (2y2 )2
= x4 − 4y4
Easy pre algebra Common factors of Monomials help:
Example 1:
Factorize m2 - 16n2
Solution:
We have m2- 16n2 = (m)2- (4n)2
= (m+4n) (m-4n)
Example 2:
Factorize 625a2-(x-y)2
Solution:
We have = [25a+(x-y)] [25a-(x-y)]
= (25a+x-y) (25a-x+y)
Example 3:
Factorize9 x4 -9 y4
Solution:
We have 9[x4- y4 ] = 9[(x2)2 - (y2)2
=9[ (x2 + y2) (x2 - y2)]
=9[ (x2 + y2) (x - y) (x + y)] `:.` Q [x2 - y2 = (x - y). (x + y)]
Here, we note that the given binomial is complete by factorized since none of the factors can further be expressed as product of two expressions. We therefore, say that an expression is said to be completely factorized if none of the factors can be further factorized, expressed as a product of two expressions with lowest exponents of terms.
Example 3:
Find the greatest common factors of 2x5 and8 x2 and then factorize 2x5+8x2
Solution:
Here, the largest numbers that divides the coefficients of 2x5 and 8x2 is 2.
The highest power of x that is a factor of x5 and x2 is x2 .
The greatest common factor of 2x5 and 8x2 is 8x2
Thus, 2x5 + 8x2 = ( 2x2.x3) +( 2x2.4)
= 2x2 (x3 + 4)
So, given expression can be expressed as the product of two factors one of which is the greatest common factor.
Practice problem for easy pre algebra help:
1.Factorize 4x2 – 9
Answer: (2x+3) (2x-3)
2.Find the value of x if 6x = 252 -172
Answer: 56
I like to share this pre algebra practice online with you all through my blog.
Let us learn a easy way of pre algebra help. Easy Pre algebra is a common name for a course in middle school mathematics. easy Pre-algebra often includes some basic subject from geometry, mostly the kinds that further understanding of algebra and show how it is used, such as area, volume, and perimeter. easy included New types of numbers such as integers, fractions, decimals and negative numbers and Simple (integer) roots and powers.(Source.Wikipedia)
Easy pre algebra Special products help:
Let us consider three special product which occur very frequently in algebra They are :
(i) (a+b)2 =a2+2ab+b2
(ii) (a-b)2 =a2 -2ab +b2
(iii) (a+b)(a+b)=a2+b2
Examples:
(i) (5+ 2)2 = 52 + (2 *5 *2) + 22 or 49 = 49 or 72
(ii) (5− 2)2 = 52 − (2 *5* 2) + 22 or9 = 9 or 32
(iii) (5+ 2)(5− 2) = 52 − 22 or21 = 21
Example 1 :
Evaluate(a) (2x + 3y)2 (b) (x2 + 2y2 )(x2 − 2y2 )
(a) (2x + 3y)2 = (2x)2 + 2 ( 2x 3y )+ (3y)2
= 4x2 +12xy + 9y2
(b) (x2 + 2y2 )(x2 − 2y2 ) = (x2 )2 − (2y2 )2
= x4 − 4y4
Easy pre algebra Common factors of Monomials help:
Example 1:
Factorize m2 - 16n2
Solution:
We have m2- 16n2 = (m)2- (4n)2
= (m+4n) (m-4n)
Example 2:
Factorize 625a2-(x-y)2
Solution:
We have = [25a+(x-y)] [25a-(x-y)]
= (25a+x-y) (25a-x+y)
Example 3:
Factorize9 x4 -9 y4
Solution:
We have 9[x4- y4 ] = 9[(x2)2 - (y2)2
=9[ (x2 + y2) (x2 - y2)]
=9[ (x2 + y2) (x - y) (x + y)] `:.` Q [x2 - y2 = (x - y). (x + y)]
Here, we note that the given binomial is complete by factorized since none of the factors can further be expressed as product of two expressions. We therefore, say that an expression is said to be completely factorized if none of the factors can be further factorized, expressed as a product of two expressions with lowest exponents of terms.
Example 3:
Find the greatest common factors of 2x5 and8 x2 and then factorize 2x5+8x2
Solution:
Here, the largest numbers that divides the coefficients of 2x5 and 8x2 is 2.
The highest power of x that is a factor of x5 and x2 is x2 .
The greatest common factor of 2x5 and 8x2 is 8x2
Thus, 2x5 + 8x2 = ( 2x2.x3) +( 2x2.4)
= 2x2 (x3 + 4)
So, given expression can be expressed as the product of two factors one of which is the greatest common factor.
Practice problem for easy pre algebra help:
1.Factorize 4x2 – 9
Answer: (2x+3) (2x-3)
2.Find the value of x if 6x = 252 -172
Answer: 56
I like to share this pre algebra practice online with you all through my blog.