Question

1. How can we find the value of these expressions without actually multiplying?
Use suitable identities to find the answer. ​

Answer 1

Answer:

1) 301 × 302 = 90902

2)(5x-y)²

=2(5-y)

10 x - 2 y .

hope it's helpful for u ok

Answer 2

Step-by-step explanation:

Solutions :-

A)

Given that 301×302

It can be written as (300+1)×(300+2)

It is in the form of (x+a)(x+b)

Where , x = 300 , a = 1 and b = 2

We know that

(x+a)(x+b) = x²+(a+b)x+ab

Now,

(300+1)×(300+2)

= (300)²+(1+2)(300)+(1×2)

= 90000+900+2

= 90902

Therefore, 301×302 = 90902

B)

Given that (5x-y)²

This is in the form of (a-b)²

Where, a = 5x and b = y

We know that

(a-b)² = a²-2ab+b²

Now,

(5x-y)²

= (5x)²-2(5x)(y)+(y)²

= 25x²-10xy+y²

Therefore, (5x-y)² = 25x²-10xy+y²

C)

Given that 104²

It can be written as (100+4)²

This is in the form of (a+b)²

Where, a = 100 and b = 4

We know that

(a+b)² = a²+2ab+b²

Now,

104²

= (100)²+2(100)(4)+4²

= 10000+800+16

= 10816

Therefore, 104² = 10816

Answers :-

A) 90902

B) 25x²-10xy+y²

C) 10816

Used Identities :-

→ (x+a)(x+b) = x²+(a+b)x+ab

→ (a+b)² = a²+2ab+b²

→ (a-b)² = a²-2ab+b²