Identify the terms, their coefficients for each of the following expressions:

1. 5xyz² - 3zy                       

2. 1+ x + x²                       

3. 4x² y² - 4x² y² z²

4. 3 - pq + qr - rp             

5.  +  – xy               

6. 0.3a – 0.6ab + 0.5b

Classify the following polynomials as monomials, binomials, trinomials.

Which polynomials do not fit in any of these three categories:

1. x + y,

2. 1000,

3. x + x² + x³ + x⁴,

4. 7 + y + 5x,

5. 2y – 3y²,

6. 2y - 3y + 4y,   

7. 5x – 4y + 3xy,

8. 4z – 15z²,  

9. ab + bc + cd + da,   

10. pqr,

11. p² q + pq², 

12. 2p + 2q

Add the following:

1. ab – bc, bc – ca, ca - ab

2. a - b + ab, b - c + bc, c - a + ac

3. 2p² q² - 3pq + 4, 5 + 7pq - 3p² q²

4. l² + m², m² + n², n² + l² + 2lm + 2mn + 2nl

(a) Subtract: 4a – 7ab + 3b + 12 from 12a – 9ab + 5b - 3

(b) Subtract: 3xy + 5yz - 7zx from 5xy – 2yz – 2zx + 10xyz

(c) Subtract: 4p² q - 3pq + 5pq² - 8p + 7q – 10 from 18 – 3p – 11p + 5pq – 2pq² + 5p² q

Find the product of the following pairs of monomials:

1. 4,7p             

2. -4p, 7p         

3. -4p, 7pq            

4. 4p³, -3p           

4. 4p, 0

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:

1. (p, q),

2. (10m, 5n),

3. (20x², 5y²),

4. (4x, 3x),

5. (3mn, 4np)

Complete the table of products:

                

 

 

Obtain the volume of rectangular boxes with the following length, breadth and height respectively:

1. 5a, 3a², 7a⁴          

2. 2p, 4q, 8r         

3. xy, 2x² y, 2xy²             

4. a, 2b, 3c

Obtain the product of:

1. xy, yz, zx              

2. –a, a², a³               

3. 2, 4y, 8y², 16y³                          

4. a, 2b, 3c, 6abc

5. m, -mn, mnp

Carry out the multiplication of the expressions in each of the following pairs:

1. 4p, q + r                        

2. ab, a - b                           

3. a + b, 7a² b²                

4. a² - 9, 4a         

5. pq + qr + rp, 0

Complete the table:

                  

Find the product:

1. a² × 2a²² × 4a²⁶                    

2. (2xy ÷ 3) × (-9x² y² ÷ 10)                       

3. (-10pq³ ÷ 3) × (6p³ q ÷ 5)

4. x × x² × x³ × x⁴

(a) Simplify: 3x (4x - 5) + 3 and find values for 1. x = 3 2. x = 1/2

(b) Simplify: a (a² + a + 1) + 5 and find its value for 1. a = 0 2. a =1 3. a = -1.

(a) Add: p (p - q), q (q - r) and r (r – p)                    

(b) Add: 2x (z - x – y) and 2y (z -y – zx)

(c) Subtract: 3l (l - 4m + 5n) from 4l (10n – 3m + 2l)

(d) Subtract: 3a (a + b + c) – 2b (a – b + c) from 4c (-a + b + c)

Multiply the binomial

1. (2x + 5) and (4x - 3)                   

2. (y - 8) and (3y - 4)           

3. (2.5l – 0.5m) and (2.5l + 0.5m)

4. (a + 3b) and (x + 5)                  

5. (2pq + 3q²) and (3pq – 2q²)

6. ((3a² ÷ 4) + 3b²) and 4(a² – (2b² ÷ 3))

Find the product:

1. (5 – 2x) × (3 + x)                                 

2. (x + 7y) × (7x - y)    

3. (a² + b) × (a + b²)                               

4. (p² – q²) × (2p + q)

Simplify:

1. (x² - 5) × (x + 5) + 25

2. (a² + 5) × (b² + 3) + 5

3. (t + s²) × (t² - s)

4. (a + b) × (c - d) + (a - b) × (c + d) + 2(ac + bd)

5. (x + y) × (2x + y) + (x + 2y) × (x - y)

6. (x + y) × (x² – xy + y²)

7. (1.5x – 4y) × (1.5x + 4y + 3) – 4.5x + 12y

8. (a + b + c) × (a + b - c)

Use a suitable identity to get each of the following products:

1. (x + 3) × (x + 3)      

2. (2y + 5) × (2y + 5)      

3. (2a - 7) × (2a - 7)      

4. (3a – ) × (3a – )

5. (1.1m – 0.4) × (1.1m + 0.4)                      

6. (a² + b²) × (-a² + b²)         

7. (6x - 7) × (6x + 7)

8. (-a + c) × (-a + c)                          

9. (  + ) × (  + )       

10. (7a – 9b) × (7a – 9b)

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products:

1. (x + 3) (x + 7)      

2. (4x + 5) (4x + 1)        

3. (4x - 5) (4x - 1)         

4. (4x + 5) (4x - 1)

5. (2x + 5y) (2x + 3y)     

6. (2a² + 9) (2a² + 5)           

7. (xyz - 4) (xyz - 2)

Find the following squares by using identities:

1. (b - 7)²                        

2. (xy + 3z)²               

3. (6x² – 5y)²                          

4. (  + )²  

5. (0.4p – 0.5q)²          

6. (2xy + 5y)²

Simplify:

1. (a² – b²)²            

2. (2x + 5)² – (2x - 5)²            

3. (7m – 8n)² + (7m + 8n)² 

4. (4m + 5n)² + (5m + 4n)²      

5. (2.5p – 1.5q)² – (1.5p – 2.5q)²    

6. (ab + bc)² – 2ab² c                 

7. (m² – n² m²) + 2m³ n²

Show that:

1. (3x + 7)² – 84x = (3x - 7)²

2. (9p – 5q)² + 180pq = (9p + 5q)²

3. (4  – 3 )² + 2mn = 16  + 9

4. (4pq + 3q)² - (4pq - 3q)² = 48pq²

5. (a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0

Using identities, evaluate:

1. 71²                     

2. 99²                    

3. 102²                

4. 998²         

5. 5.2²        

6. 297 × 303  

7. 78 × 82          

8. 8.9²                 

9. 1.05 × 9.5

Using a² – b² = (a + b) (a - b), find:

1. 51² – 49²          

2. (1.02)² – (0.98)²           

3. 153² – 147²           

4. 12.1² – 7.9²

Using (x + a) (x + b) = x² + (a + b) x + ab, find

1. 103 × 104                    

2. 5.1 × 5.2             

3. 103 × 98             
4. 9.7 × 9.8