Question

Evaluate the following using suitable identities: 1) (3a)²-(2b)² (50 brainly points giveaway for the first correct answer​

Answer 1

Step-by-step explanation:

1) (3a)² - (2b)²

we have to evaluate by using suitable identity .

So, we will use here this identity

• a² - b² = (a-b) (a+b)

Now, evaluating

Let , a = 3a

and , b = 2b

➻ (3a)² - (2b)²

➻ (3a - 2b) ( 3a + 2b)

• So, the required answer is (3a-2b) (3a+2b)

Extra Information !!

Some More identities!!

• (a + b)² = a² + b² +2ab

• ( a - b )² = a² + b² -2ab

• ( a² - b² ) = ( a - b ) ( a + b )

• ( a +b +c)² = (a² + b² + c²) + 2(ab + bc +ca)

• (a + b)³ = a³ + b³ + 3ab(a+b)

• (a-b)³ = a³ - b³ -3ab(a-b)

• ( a³ + b³) = (a+b) (a²-ab +b²)

• (a³ - b³) = (a -b) (a² + ab + b²)

Answer 2

Answer:

(3a + 2b) (3a - 2b)

Step-by-step explanation:

Here, we have been asked to evaluate the following using suitable identity:

• $\sf{{(3a)}^{2}-{(2b)}^{2}}$

The identity we have to use here:

$\implies\quad\sf{{a}^{2}-{b}^{2}=(a+b)(a-b)}$

Let us consider a as 3a and b as 2b. So, equating the values.

$\\\twoheadrightarrow\quad\underline{\boxed{\bold{{(3a)}^{2}-{(2b)}^{2}=(3a+2b)(3a-2b)}}}$

❝ Therefore, (3a)²-(2b)² is equal to (3a + 2b) (3a - 2b). ❞

Additional Information:

More identities to know:

$\twoheadrightarrow\quad\sf{{(a+b)}^{2}={a}^{2}+{b}^{2}+2ab}$

$\\\twoheadrightarrow\quad\sf{{(a-b)}^{2}={a}^{2}+{b}^{2}-2ab}$

$\\\twoheadrightarrow\quad\sf{{a}^{2}+{b}^{2}={(a+b)}^{2}={(a+b)}^{2}-2ab}$

$\\\twoheadrightarrow\quad\sf{{(a+b+c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2ab+2bc+2ca}$

$\\\twoheadrightarrow\quad\sf{{(a-b-c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}-2ab+2bc-2ca}$