Question

(2a-3b)(2a+3b)(4a^2+9b^2)​

Answer 1

Answer:

16a⁴ - 81b⁴

Step-by-step explanation:

(2a-3b)(2a+3b)(4a²+9b²)

= [(2a)² - (3b)²](4a²+9b²)

/* By algebraic identity:

(x-y)(x+y) = x²-y² */

= (4a²-9b²)(4a²+9b²)

= (4a²)² - (9b²)²

= 16a⁴ - 81b⁴

Therefore,

(2a-3b)(2a+3b)(4a²+9b²)

= 16a⁴ - 81b⁴

•••♪

Answer 2

$\huge\sf{Answer:-}$

$(2a - 3b)(2a + 3b)(4a {}^{2} + ab {}^{2} ) \\ =( 2a ){}^{2} - (3b) {}^{2} (4a {}^{2} + 9b {}^{2} )$

Algebric Identity:-

$\sf (x - y)(x + y) = x {}^{2} - y {}^{2} \\ \sf = (4a {}^{2} - 9b {}^{2} )(4a {}^{2} + 9b {}^{2} ) \\ \sf = (4a {}^{2} - (9b {}^{2} ) {}^{2} \\ \sf = 16a {}^{4} - 81b {}^{4}$

Hence,

$\sf (2a - 3b)(2a + 3b)(4a {}^{2} + 9b {}^{2} ) \\ \sf = > 16a {}^{4} - 81b {}^{4}$