FACTORIZATION OF POLYNOMIALS WITH CUBE FORMULA IS ALGEBRAIC IDENTITIES
About "Factorization of Polynomials With Cube Formula in Algebraic Identities"
Factorization of Polynomials With Cube Formula in Algebraic Identities :
Here we are going to see some example problems on factoring polynomials with cube formula in algebraic identities.
Factorization of Polynomials With Cube Formula in Algebraic Identities - Examples
Question 1 :
Factorise the following
(i) 8x3 + 125y3
Solution :
8x3 + 125y3 = (2x)3 + (5y)3
a3 + b3 = (a + b)(a2 - ab + b2)
(2x)3 + (5y)3 = (2x + 5y)((2x)2 - (2x)(5y) + (5y)2)
= (2x + 5y)(4x2 - 10xy + 25y2)
(ii) 27x3 - 8y3
Solution :
27x3 - 8y3 = (3x)3 - (2y)3
a3 - b3 = (a - b)(a2 + ab + b2)
(3x)3 - (2y)3 = (3x - 2y)((3x)2 + (3x)(2y) + (2y)2)
= (3x - 2y)(9x2 + 6xy + 4y2)
(iii) a6 - 64
Solution :
a6 - 64 = (a2)3 - 43
a3 - b3 = (a - b)(a2 + ab + b2)
a = a2 and b = 4
(a2)3 - 43 = (a2 - 4) ((a2)2 + a2 (4) + 42)
= (a2 - 4) ((a4 + 4a2 + 16)
= (a2 - 4) ((a2 + 4)2 - (2a)2)
= (a + 2)(a - 2) ((a2 + 4) + 2a)((a2 + 4) - 2a)
= (a + 2)(a - 2) ((a2 + 2a + 4)((a2 - 2a + 4)
Question 2 :
Factorise the following:
(i) x3 + 8y3 + 6 xy - 1
Solution :
= x3 + 8y3 + 6 xy - 1
= x3 + (2y)3 + (-1)3 - 3 x(2y)(-1)
a3 + b3 + c3 - 3abc = (a + b + c)(a2+b2+c2-ab-bc-ca)
= (x + 2y - 1) (x2 + 4y2 + 1 - 2xy + 2y - x)
(ii) l3 - 8m3 - 27n3 - 18 lmn
Solution :
= l3 - 8m3 - 27n3 - 18 lmn
= l3 + (-2m)3 + (-3n)3 - 3 (1)(-2m)(-3n)
a3 + b3 + c3 - 3abc = (a + b + c)(a2+b2+c2-ab-bc-ca)
= (l - 2m - 3n) (l2 + 4m2 + 9n2 + 2lm - 6mn + 3ln)
After having gone through the stuff given above, we hope that the students would have understood, "Factorization of Polynomials With Cube Formula in Algebraic Identities"
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Algebra Worksheets in Math
Sep 23, 19 07:57 AM
Algebra Worksheets in Math - Concepts and practice questions with step by step solution
-
Solving Word Problems with Nature of Roots of Quadratic Equation
Sep 23, 19 05:08 AM
Solving Word Problems with Nature of Roots of Quadratic Equation - Concept and examples with step by step solution
-
Nature of Roots of Quadratic Equation Discriminant Examples
Sep 23, 19 04:47 AM
Nature of Roots of Quadratic Equation Discriminant Examples - Concept and examples with step by step solution
