Answer:
The product of (4 +5x)(4-5x) is 16 - 25x².
Step-by-step explanation:
To find: Product of (4 +5x)(4-5x) using suitable identities.
Identity used : a² - b² = (a+b)(a-b)
Solution:
(4 +5x)(4-5x)
= (4)² - (5x)².........(using identity a² - b² = (a+b)(a-b))
(Here, a = 4 and b = 5x)
= 16 - 25x²
The given question can be solved without the use of the identity
a² - b² = (a+b)(a-b) as well.
Alternative Solution (without use of identity)-
(4 +5x)(4-5x)
(As (a+b)(c+d) = a(c+d)+b(c+d) )
= 4(4-5x) + 5x(4-5x)
= 16 - 20x + 20x - 25x²
= 16 - 25x²
Hence, the product of (4 +5x)(4-5x) is 16 - 25x².
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