Question

find the continued product using the identities (5a - 2b) (5a+2b) (25a2 - 4b2)

Answer 1

(5a-2b)(5a+2b)(25a^2-4b^2)
=(25a^2-4b^2)(25a^2-4b^2)
=625a^4+16b^4-200a^2b^2


Hope you are satisfied...!!

Answer 2

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Find the continued product using the identities:

(5a - 2b) (5a+2b) (25a² - 4b²)

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The continued product.

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Identity⫸}}}}}}$

(a-b)(a+b) = (a²+b²)

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Solution⫸}}}}}}$

(5a - 2b) (5a + 2b) (25a² - 4b²)

(5a - 2b) (5a + 2b)

= {(5a)² - (2b)²}

= (25a² - 4b²) $\orange{★}$

(25a² - 4b²) (25a² - 4b²)

= 25a²(25a²-4b²)-4b²(25a² - 4b²)

= 625a²-100a²b²-100a²b²-16b⁴

= 625a²-200a²b²-16b² $\red{★}$

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Hence⫸}}}}}}$

(5a - 2b) (5a + 2b) (25a² - 4b²)

= 625a²-200a²b²-16b²

${\large{\fcolorbox{aqua}{navy}{\fcolorbox{yellow}{blue}{\bf{\color{yellow}{⫷Therefore⫸}}}}}}$

The value of {(5a - 2b) (5a + 2b) (25a² - 4b²)} is 625a²-200a²b²-16b².

${\huge\mathtt \pink{Done࿐}}\\{\huge\mathfrak \green{Hope\:this\: helps\:you.}}\\{\huge\mathfrak \orange{Have\:a\: nice\:day.}}$