Expand using suitable identities: [(4/5)a + (5/4)b]²

Solution:

Given, [(4/5)a + (5/4)b]²

Using standard identity: (x + y)² = x² + 2xy + y²

Here, x = (4/5)a and y = (5/4)b

[(4/5)a + (5/4)b]² = [(4/5)a]² + 2[(4/5)a][(5/4)b] + [(5/4)b]²

= (16/25)a² + 2ab + (25/16)b²

✦ Try This: Expand using suitable identities: [(2/7)p - (7/2)q]²

Given, [(2/7)p - (7/2)q]²

Using standard identity: (a - b)² = a² - 2ab + b²

[(2/7)p - (7/2)q]² = [(2/7)p]² - 2(2/7)p(7/2)q + [(7/2)q]²

= 4p²/49 - 2pq + 49q²/4

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 85(iii)

Expand using suitable identities: [(4/5)a + (5/4)b]²

Summary:

Expanding [(4/5)a + (5/4)b]² we get, (16/25)a² + 2ab + (25/16)b²

☛ Related Questions:

• Expand using suitable identities: [(2/3)x - (3/2)y]²
• Expand using suitable identities: [(4/5)p + (5/3)q]²
• Expand using suitable identities: (x + 3)(x + 7)