Question

Find the product using suitable identities: (4 +5x)(4-5x).
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Answer 1

Answer:

[4+5x][4-5x]

[a+b][a-b]=a²-b²

[4]²-[5x]²

16-25x²

Answer 2

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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