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Factorization and algebraic fractions

Total questions: 10

Worksheet time: 8mins

Name
Class
Date
1.

 (a+2b)2−(a2−b2)\left(a+2b\right)^2-\left(a^2-b^2\right)  

a)

 3b23b^2  

b)

 5b2+4ab5b^2+4ab  

c)

 5b2+2ab5b^2+2ab  

d)

 a2+4b2a^2+4b^2  

2.

Simplify  (x−2y)−4(3x−y)\left(x-2y\right)-4\left(3x-y\right)  

a)

 −11x−6y-11x-6y  

b)

 −11x−3y-11x-3y  

c)

 −11x−y-11x-y  

d)

 −11x+2y-11x+2y  

3.

 3p+41−p\frac{3}{p}+\frac{4}{1-p}  

a)

 3+4p1−p\frac{3+4p}{1-p}  

b)

 3+p1−p\frac{3+p}{1-p}  

c)

 3+pp(1−p)\frac{3+p}{p\left(1-p\right)}  

d)

 3+4p23+4p^2  

4.

 (4m−5n)(5m+4n)\left(4m-5n\right)\left(5m+4n\right)  

a)

 20m2+9mn−20n220m^2+9mn-20n^2  

b)

 20m2−9mn−20n220m^2-9mn-20n^2  

c)

 20m2−41mn−20n220m^2-41mn-20n^2  

d)

 20m2−41mn+20n220m^2-41mn+20n^2  

5.

 p2+(3p+q)(3p−q)p^2+\left(3p+q\right)\left(3p-q\right)  

a)

 10p2−q210p^2-q^2  

b)

 10p2+q210p^2+q^2  

c)

 9p2−q29p^2-q^2  

d)

 9p2+6pq−q29p^2+6pq-q^2  

6.

Express  3s2−5s−2s+97\frac{3s^2-5}{s}-\frac{2s+9}{7}  as a single fraction in its simplest form

a)

 19s2−9s−357s\frac{19s^2-9s-35}{7s}  

b)

 19s2−9s−35s\frac{19s^2-9s-35}{s}  

c)

 3s2−2s−14s\frac{3s^2-2s-14}{s}  

d)

 3s2−2s+4s\frac{3s^2-2s+4}{s}  

7.

 6(2x−7)−(10−6x)26\left(2x-7\right)-\left(10-6x\right)^2  

a)

 −142+132x−36x2-142+132x-36x^2  

b)

 100+132x−36x2100+132x-36x^2  

c)

 −142+12x+36x2-142+12x+36x^2  

d)

 100+12x+36x2100+12x+36x^2  

8.

Express  p+2q2pq−p+1p\frac{p+2q}{2pq}-\frac{p+1}{p}  as a single fraction in its simplest form

a)

 1−2q2q\frac{1-2q}{2q}  

b)

 p−2pq2pq\frac{p-2pq}{2pq}  

c)

 p−2pq+4q2pq\frac{p-2pq+4q}{2pq}  

d)

 p−2pq−4q2pq\frac{p-2pq-4q}{2pq}  

9.

 2(2x−3)−(x−2)2\left(2x-3\right)-\left(x-2\right)  

a)

 3x−43x-4  

b)

 3x−83x-8  

c)

 4x−54x-5  

d)

 3x−23x-2  

10.

 (3y−2)(2y+3)\left(3y-2\right)\left(2y+3\right)  

a)

 6y2−5y−66y^2-5y-6  

b)

 6y2+5y−66y^2+5y-6  

c)

 6y2+13y−66y^2+13y-6  

d)

 6y2−13y−66y^2-13y-6