Question

Find the value of z if: xyz = (4x + 5y)² - (4x- 5y)²​

Answer 1

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Given:

• $xyz = (4x + 5y)^2 - (4x- 5y)^2$

To find:

• Value of z.

Solution:

$xyz = (4x + 5y)^2 - (4x- 5y)^2 --------(i)$

$\text{ We know that, a^2 - b^2 = (a + b)*(a - b) . And, a = 4x + 5y and b= 4x - 5y. \\ So,}$

$\implies (4x + 5y)^2 - (4x- 5y)^2 = (4x + 5y + 4x - 5y)*(4x + 5y - 4x + 5y)$

$\implies (4x + 5y)^2 - (4x- 5y)^2 = 8x * 10y$

$\implies (4x + 5y)^2 - (4x- 5y)^2 = 80xy ---------(ii)$

$\text{ Now, putting (ii) in (i), we get, }$

$\implies xyz = 80xy$

$\implies \textbf{z = 80}$

Formula Used:

• $a^2 - b^2 = (a + b)*(a - b)$

HOPE IT HELPS!!!