Question

EVALUATE :-

(2a-5b) (2a + 5b) (4a² +25b²)

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Answer 1

GIVEN :-

• (2a - 5b) (2a + 5b) (4a² + 25b²)

TO FIND :-

• The value of (2a - 5b) (2a + 5b) (4a² + 25b²).

SOLUTION :-

Firstly , Let's divide the equation into two parts,

⇒ [(2a - 5b) (2a + 5b)] [(4a² + 25b²)]

Now by using identity (a + b)(a - b) = a² - b².

⇒ [ (2a)² - (5b)² ] [ 4a² + 25b² ]

⇒ (4a² - 25b²)(4a² + 25b²)

Now by using identity (a + b)(a - b) = a² - b².

⇒ (4a²)² - (25b²)²

⇒ 16a⁴ - 625b⁴

⇒ (2a - 5b) (2a + 5b) (4a² + 25b²) = 16a⁴ - 625b⁴.

Hence the value of (2a - 5b) (2a + 5b) (4a² + 25b²) is 16a⁴ - 625b⁴.

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Verified Answer ✅ .

Answer 2

$(2a - 5b)(2a + 5b)(4 {a}^{2} + 25b {}^{2} ) \\ \\ (x + y)(x - y) = {x}^{2} - {y}^{2} \\ \\ (2a - 5b)(2a + 5b) = {(2a)}^{2} - {(5b) }^{2} \\ = 4 {a}^{2} - 25 {b}^{2} \\ \\ (2a - 5b)(2a + 5b)(4 {a}^{2} + 25b {}^{2} ) \\ \\ = (4 {a}^{2} - 25 {b}^{2} )(4 {a}^{2} + 25 {b}^{2} ) \\ \\ = 16 {a}^{4} - 625 {b}^{4}$