Expand using suitable identities: [(2x/3) - (2/3)] [(2x/3) + (2a/3)]
Solution:
Given, [(2x/3) - (2/3)] [(2x/3) + (2a/3)]
Using standard identity: (x + a) (x + b) = x² + (a + b)x + ab
Here, a = - (2/3) and b = (2a/3)
[(2x/3) - (2/3)] [(2x/3) + (2a/3)]
= [(2x/3)]² + {[-(2/3) + (2a/3)](2x/3)} + [ -(2/3) × (2a/3)]
= (4x²/9) + {[(2a - 2)/3](2x/3)} - 4a/9
= (4x²/9) + {[2(a - 1)/3](2x/3)} - 4a/9
= (4x²/9) + [4x(a - 1)/9] - 4a/9
✦ Try This: Expand using suitable identities: [(4x/5) - (2/3)] [(4x/5) - (5/2)]
Given, [(4x/5) - (2/3)] [(4x/5) - (5/2)]
Using standard identity: (x + a) (x + b) = x² + (a + b)x + ab
[(4x/5) - (2/3)] [(4x/5) - (5/2)] = (4x/5)² + (-2/3 - 5/2) (4x/5) + (-2/3) (-5/2)
= 16x²/25 - (38/15)x+(5/3)
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9
NCERT Exemplar Class 8 Maths Chapter 7 Problem 85(ix)
Expand using suitable identities: [(2x/3) - (2/3)] [(2x/3) + (2a/3)]
Summary:
Expanding [(2x/3) - (2/3)] [(2x/3) + (2a/3)] we get, (4x²/9) + [4x(a - 1)/9] - 4a/9
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