FACTORING BY GROUPING WORKSHEET
About "Factoring by grouping worksheet"
Factoring by grouping worksheet :
Here we are going to see some practice questions on factoring.
Factoring by grouping worksheet - Practice questions
(1) Factorise the following expression
2a3 - 3a2 b + 2a2 c
(2) Factorise the following expression
16x + 64x2y
(3) Factorise the following expression
10x3 + 25x4y
(4) Factorise the following expression
xy - xz + ay - az
(5) Factorise the following expression
p2 + pq + pr + qr
(6) Factorise the following expression
4a - 8b + 5ax - 10bx
Factoring by grouping worksheet - Solution
Question 1 :
Factorise the following expression
2a3 - 3a2 b + 2a2 c
Solution :
= 2a3 - 3a2 b + 2a2 c
In the above three terms, we have the common variable "a2".
By factor out "a2", we get
= a2 (2a - 3b + 2c)
Question 2 :
Factorise the following expression
16x + 64x2y
Solution :
= 16x + 64x2y
In the above two terms, we have the common term "16x".
By factor out "16x", we get
= x (16) + 16x (4xy)
= 16x (1 + 4xy)
Question 3 :
Factorise the following expression
10x3 + 25x4y
Solution :
= 10x3 + 25x4y
In the above two terms, we have the common term "5x3".
By factor out "5x3", we get
= 5x3 (2) + 5x3 (5xy)
= 5x3 (2 + 5xy)
Question 4 :
Factorise the following expression
xy - xz + ay - az
Solution :
= xy - xz + ay - az
Let us consider the first two terms as one group and third fourth terms as other group.
In the first two terms, we have the common variable "x".
In the third and fourth terms, we have the common variable "a"
= x (y - z) + a (y - z)
= (x + a) (y - z)
Question 5 :
Factorise the following expression
p2 + pq + pr + qr
Solution :
= p2 + pq + pr + qr
Let us consider the first two terms as one group and third fourth terms as other group.
In the first two terms, we have the common variable "p".
In the third and fourth terms, we have the common variable "r"
= p (p + q) + r (p + q)
= (p + r) (p + q)
Question 6 :
Factorise the following expression
4a - 8b + 5ax - 10bx
Solution :
= 4a - 8b + 5ax - 10bx
We have 4 terms in the given algebraic expression.Now we are going to split into two groups.
4a and -8b are in one group (Group 1)
5ax and -10bx are in the other group(Group 2)
Common term of 1st group is 4
Common term of 2nd group is 5x
= 4 (a - 2b) + 5x (a - 2b)
= (4 + 5x) (a - 2b)
After having gone through the stuff given above, we hope that the students would have understood "Factoring by grouping worksheet".
Apart from the stuff given above, if you want to know more about "Factoring by grouping worksheet", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM 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
