Question

Evaluate:

1: (3a²-4b²)(8a²-3b²)

2: (a+bc)(a-bc)(a²+b²c²)​

Answer 1

-(3a²-4b²)(8a²-36²)

-3(8a² − 3b²) a² − 4(8a² − 3b²) · b²

-3(8a²3b²) a² - 4(8a² − 3b²) · b² 24a4-9a²b² - 4(8a²-3b²). b²

-24a²-9a²b²-4(8a²-3b²). b²

-24a¹ – 9a²b² −32a²b² + 12b⁴

-24a²-9a²b²-32a²b² +12b⁴

-24a⁴-41a²b² +12b⁴

Answer 2

Answer:

1. 24a⁴ - 41a²b² + 12b⁴
2. a⁴ - b⁴c⁴

Step-by-step explanation:

Given Questions :

1. (3a² - 4b²)(8a² - 3b²)
2. (a + bc)(a - bc)(a² + b²c²)

To find :

The values of the given questions

Solution :

1. (3a²-4b²)(8a²-3b²)

=> 3a² × (8a²-3b²) - 4b² × (8a²-3b²)

=> 24a⁴ - 9a²b² - 32a²b² + 12b⁴

=> 24a⁴ - 41a²b² + 12b⁴

Thus,

$\boxed {\boxed {\mathbf {(3a^2 - 4b^2)(8a^2-3b^2) = 24a^4 - 41a^2b^2 + 12b^4}}}$

______________

2. (a + bc)(a-bc)(a²+b²c²)

We know that,

$\boxed {(x+y)(x-y) = x^2-y^2}$

Here, for (a+bc)(a-bc), x = a and y = bc

So, this turns into,

(a²-b²c²)(a²+b²c²)

Again applying the same formula

Here, x = a² and y = b²c²

=> (a²-b²c²)(a²+b²c²)

=> (a⁴ - b⁴c⁴)

Thus,

$\boxed {\boxed {\mathbf {(a+bc)(a-bc)(a^2+b^2c^2) = a^4-b^4c^4}}}$

Hope it helps!