Class 8 Maths Algebraic Expressions assignment

Amend Education Academy 9999908238

Solved Assignment Algebric expressions

Basic Algebra Formulas:

Algebra is the part of mathematics which involves in manipulating equations or algebraic expressionsA list of given  basic algebra formulas can be used for the  application process, helps in understanding of the concept.

List of Algebraic Formulas :
The following are some of the important algebraic identities or expression used in class 8^th and 9^th maths

      1.  (a + b)² = a² + 2ab + b²

      2.  (a - b)²  = a² - 2ab + b²

      3.  (a + b) (a - b)  = a2 - b2

      4.  (x + a)(x + b)  = x2 + (a + b)x + ab

      5.  (x + a)(x - b)  = x² + (a - b)x - ab

      6.  (x - a)(x + b)  = x² + (b - a)x - ab

      7.  (x - a)(x - b)  = x²  - (a + b)x + ab

      8.  (a + b)³  = a³ + b³ + 3ab(a + b)

      9.  (a - b)³  =  a³ - b³ - 3ab(a - b)

     10.  (x + y + z)²  = x² + y² + z² + 2xy + 2yz + 2xz

     11.  (x + y - z)²  =  x² + y² + z² + 2xy - 2yz - 2xz

     12.  (x - y + z)²  = x² + y² + z² - 2xy - 2yz + 2xz

     13.  (x - y - z)²  = x² + y² + z² - 2xy +  2yz - 2xz

     14.  x³ + y³ + z³ - 3xyz  = (x + y + z)(x² + y² + z² - xy - yz -xz)

     15.  x² + y²  = 12 [(x + y)² + (x - y)²]

     16.  (x + a) (x + b) (x + c) = x³ + (a + b +c)x² + (ab + bc + ca)x + abc

     17.  x³ + y³ = (x + y) (x² - xy + y²)

     18.  x³ - y³  = (x - y) (x² + xy + y²)

     19.  x² + y² + z² -xy - yz - zx = 12 [(x-y)² + (y-z)² + (z-x)²]

Questions

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

(i) 5a, 3a², 7a⁸ (ii) 2p, 4q, 8r (iii) xy, 2x²y, 2xy²(iv) a, 2b, 3c

2. Multiply following

i) (2x + 5) and (4x – 3) (ii) (y – 8) and (3y – 4) (iii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y

3. Use a suitable identity to get each of the following products.

(i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5) (iii) (2a – 7) (2a – 7)

4. Using identities, evaluate.

(i) 71² (ii) 99² (iii) 102²

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

(i) 103 x 104

Factorization

1. Factorise the following expressions.

(i) a² + 8a + 16  (ii) p² – 10 p + 25 (iii) 25m² + 30m + 9

2. Factorise.

(i) 4p² – 9q²  (ii) 63a² – 112b²  (iii) 49x² – 36 (iv) 16x⁵ – 144x³ (v) 25a² – 4b² + 28bc – 49c²

3. Factorise the following expressions.

(i) p² + 6p + 8   (ii) q² – 10q + 21  (iii) p² + 6p – 16

Answers

1: Volume = length x  breadth x  height

(i) 5a x 3a² x 7a⁸ = 105a¹¹

(ii) 2p x 4q x 8r = 64pqr

(iii) xy x 2x²y x 2xy² = 4x⁴y⁴

(iv) a x  2b x 3c = 6abc

2. 1. Multiply following

i) (2x + 5) and (4x – 3)

Answer: (2x + 5)(4x - 3)

= 2x x 4x - 2x x 3 + 5 x 4x - 5 x 3

= 8x² - 6x + 20x -15

= 8x² + 14x -15

(ii) (y – 8) and (3y – 4)

Answer: ( y - 8)(3y - 4)

= y x 3y - 4y - 8 x 3y + 32

= 3y² - 4y - 24y + 32

= 3y² - 28y + 32

(iii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y

Answer: = 2.25x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y

= 2.25x² - 16y²

3. Use a suitable identity to get each of the following products.

(i) (x + 3) (x + 3)

Answer: Using (a + b)² = a² + 2ab + b² we get the following equation:

= x² + 6x + 9

(ii) (2y + 5) (2y + 5)

Answer: 4y² + 20y + 25

(iii) (2a – 7) (2a – 7)

Answer: Using (a - b)² = a^{2 -} 2ab + b² we get the following equation:

= 4a² - 28a + 49

4(i)  71² = (70+1)²

Using (a + b)² = a² + 2ab + b²

= 70² + 140 + 1²

= 4900 + 140 +1= 5041

(ii) 99²

= (100 -1)²

= 100² - 200 + 1²

= 10000 - 200 + 1

= 9801

(iii) 102²

= (100 + 2)²

= 100² + 400 + 2²

= 10000 + 400 + 4

= 10404

5. (i) 103 x 104

= (100 + 3)(100 + 4)

= 100² + (3 + 4)100 + 12

= 10000 + 1200 + 12

= 11212

Factorization

1. Factorise the following expressions.

(i) a² + 8a + 16

(ii) p² – 10 p + 25

(iii) 25m² + 30m + 9

2. Factorise.

(i) 4p² – 9q²

(ii) 63a² – 112b²

(iii) 49x² – 36

(iv) 16x⁵ – 144x³

Answer:16x⁵-144x³

= x³(16x²-144)

= x³(4x+12)(4x-12)

(v) 25a² – 4b² + 28bc – 49c²

3. Factorise the following expressions.

(i) p² + 6p + 8

Asnwer: p²+6p+8

=p(p+6)+8

(ii) q² – 10q + 21

Answer: q²-10q+21

=q(q-10)+21

(iii) p² + 6p – 16

Answer: p²+6p-16

=p(p+6)-1