Question

Simplify using identities:

1) (4m + 5m)² + (5m + 4n)²

2) 297 × 303​

Answer 1

$\huge\underline\mathrm{Correct\:Question}$

★ Simplify using identities :

1. $\large\bf{(4m + 5n)^2 + (5m + 4n)^2}$
2. $\large\bf{297 × 303}$

$\huge\underline\mathrm{Answer}$

Let's have a look on the identities which will ne used here :

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

$\implies\sf{(x + a) (x + b) = x^2 + (a + b)x + ab}$

or,

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

Now, let's solve both the questions :-

1.) $\large\bf{(4m + 5n)^2 + (4n + 5m)^2}$

We have considered (4m + 5n)² as 1 and (4n + 5m)² as 2.

Let's solve “1” first :-

$\large\bf\implies{Using\: identity = (a + b)^2 = a^2 + b^2 + 2ab}$

$\large\bf\hookrightarrow{(4m + 5m)^2 = (4m)^2 + (5n)^2 + 2(4m)(5n)}$

$\large\bf\hookrightarrow{(4m + 5m)^2 = 16m^2 + 25n^2 + 40mn}$

Now,let's solve “2” :-

$\large\bf\implies{Using\: identity = (a + b)^2 = a^2 + b^2 + 2ab}$

$\large\bf\hookrightarrow{(4n + 5m)^2 = (4n)^2 + (5m)^2 + 2(4n)(5m)}$

$\large\bf\hookrightarrow{(4n + 5m)^2 = 16n^2 + 25m^2 + 40mn}$

Taking both of them together :-

$\large\bf\implies{16m^2 + 25n^2 + 40mn + 16n^2 + 25m^2 + 40mn}$

$\large\bf\implies{41m^2 + 41n^2 + 80mn}$

2.) $\large\bf{(297 × 303)}$

$\large\bf\implies{(300 - 3) × (300 + 3)}$

$\large\bf\implies{Using\:identity = (x + a) (x + b) = x^2 + (a + b)x + ab}$

$\large\bf\hookrightarrow{(300 - 3) (300 + 3) = (300)^2 + (-3 + 3)300 + (-3)(+3)}$

$\large\bf\hookrightarrow{(300 - 3) (300 + 3) = 90000 + 0 + (-9)}$

$\large\bf\hookrightarrow{(300 - 3) (300 + 3) = 89991}$

___________________________________

Extra information :-

Identities :-

$\large\bf\implies{(a-b) = a^2 + b^2 - 2ab}$

$\large\bf\implies{(a+b) = a^2 + b^2 + 2ab}$

$\large\bf\implies{(a-b)^2 = (a+b) (a-b)}$

$\large\bf\implies{(x+a) (x+b) = x^2 + (a+b)x + ab}$

Thank you!!

Answer 2

Correct question :

Simplify using identities:

1) (4m + 5n)² + (5m + 4n)²

2) 297 × 303

────────────────────────

Answer:

1) 41 m² + 41 n² + 80 mn

2) 89991

Step-by-step explanation:

1) (4m + 5n)² + (5m + 4n)²

Using the identity : (a + b)² = a² + b² + 2ab

(4m + 5n)² = (4m) ² + (5n) ² + 2 (4m) (5n)

= 16m² + 25n² + 40mn

(5m + 4n)² = (5m) ² + (4n) ² + 2 (5m) (4n)

= 25m² + 16n² + 40mn

Now, adding the like terms :

=> 16m² + 25n² + 40mn + 25m² + 16n² + 40mn

=> 41m² + 41n² + 80mn

────────────────────────

2) 297 × 303

=> (300 - 3) (300 + 3)

Using the identity : (x + a) (x + b) = x² + (a + b) x + ab

=> (300)² + (-3 + 3)300 + (-3) (3)

=> 90000 + 0 - 9

=> 89991