ONLINE TUTORIAL FOR ALGEBRA

BASIC IDENTITIES IN ALGEBRA

[ This is a tutorial on Basic Algebraic Identities. It will serve as a good revision exercise for all High School Students (from 8^th to 10^th grade)

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IDENTITY No: 1

(a + b)²  =  a² + b² + 2ab

Expand the following using the above identity

(i)  (a + 3)²

(ii)  ( P + 1)²

(iii)  ( ½ + y)²

(iv) (xy + 7)²

(v) ( x + 2y)²

(vi) ( 3a + 2b)²

(vii) (7k + 2)²

(viii) (a² + 4)²

(ix) (5a² + 2b²)²

(x) (3x + 4wyz)²

(xi)(3a + ½)²

(xii) (2a + 3b/c)²

(xiii) (¼ p + ½ q)²

(xiv) (2x³ + 4yz)²

(xv) ( 1 + 5x³y)²

IDENTITY No: 2

(a - b)² = a² + b² - 2ab

Expand the following using the above identity:

1.(i) (p – y)²

   (ii) ( m – 9)²

   (iii) (10 – 8m)²

   (iv) (5a – 2y)²

    (v) ( k – ¾ )²

   (vi) (xy – 2z)²

   (vii) (c² – 4bc)²

   (viii) (a² – b²)²

    (ix) (4a³b - 2)²

     (x) (1.1m - 7)²

(2)  Simplify : (2x + 5)² + (2x - 5)²

(3)  Simplify:  (ab - bc)² + 2ab²c

(4) Simplify : (0.4p - 0.5q)²

(5) Show that (3x + 7)² - 84x = (3x - 7)²

(6) Show that   (4pq + 3q)² - (4pq - 3q)² = 48pq²

IDENTITY No: 3

(a + b)(a - b) = a² - b²

Simplify the following using the above identity:

1 (i) ( m + 3)( m - 3)

   (ii) (7y + 1)(7y - 1)

   (iii) (2ab + c)(2ab - c)

   (iv) ( 3z + ½ )(3z – ½)

   (v) ( 5 + 4k)(5 - 4k)

   (vi) ( 3z² + w)(3z² - w)

   (vii) (y³ - 2.5)(y³ + 2.5)

 (viii)(2a³b² - 5)(2a³b² + 5)

  (ix) (a/b + b/c)(a/b - b/c)

   (x) (3abc + 0.7)(3abc - 0.7)

(2) Simplify:

    (i) (a + b)(a - b)(a² + b²)

 

   (ii)  (1 + 2a)(1- 2a)(1 + 4a²)(1 + 16a²)

   (iii) (3a + 2b)(3a - 2b) - (3b - a)(3b + a)

(3)  Prove that (a - b)(a + b) + (b - c)(b + c) + (c +a )(c - a) = 0

IDENTITY No: 4

(x + a)(x + b) = x²+ (a+b)x + ab

Simplify the following using the above identity:

(i)    (b + 5)(b + 2)

(ii)  (k + 13)(K + 5)

(iii) (y² + 6)(y2 + 5)

(iv) (3x + 5)(3x + 7)

(v)  (x + 7 )( x - 3)

(vi) (ab + 7c)(ab - 3c)

(vii) (3x + 5y) (2x + y)

(viii) (7x² + 3y)(7x² – 2y)

(ix) (2x³ + ¾ )(2x³ +1/4)

(x)  (5pqr + 5s)(5pqr - 11s)

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