Evaluate the following using suitable identities: 1) (3a)²-(2b)² (50 brainly points giveaway for the first correct answer
Home
/
Evaluate the following using suitable identities: 1) (3a)²-(2b)² (50 brainly points giveaway for the first correct answer
Verified answer
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)
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:
(3a + 2b) (3a - 2b)
Step-by-step explanation:
Here, we have been asked to evaluate the following using suitable identity:
The identity we have to use here:
[tex]\implies\quad\sf{{a}^{2}-{b}^{2}=(a+b)(a-b)} [/tex]
Let us consider a as 3a and b as 2b. So, equating the values.
[tex]\\\twoheadrightarrow\quad\underline{\boxed{\bold{{(3a)}^{2}-{(2b)}^{2}=(3a+2b)(3a-2b)}}} [/tex]
❝ Therefore, (3a)²-(2b)² is equal to (3a + 2b) (3a - 2b). ❞ [tex]\\ [/tex]
Additional Information:
More identities to know:
[tex]\twoheadrightarrow\quad\sf{{(a+b)}^{2}={a}^{2}+{b}^{2}+2ab} [/tex]
[tex]\\\twoheadrightarrow\quad\sf{{(a-b)}^{2}={a}^{2}+{b}^{2}-2ab} [/tex]
[tex]\\\twoheadrightarrow\quad\sf{{a}^{2}+{b}^{2}={(a+b)}^{2}={(a+b)}^{2}-2ab} [/tex]
[tex]\\\twoheadrightarrow\quad\sf{{(a+b+c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}+2ab+2bc+2ca} [/tex]
[tex]\\\twoheadrightarrow\quad\sf{{(a-b-c)}^{2}={a}^{2}+{b}^{2}+{c}^{2}-2ab+2bc-2ca} [/tex]