Question

Q1. Find the squares of the following number.
1. 3x + 5y
2. a+b
3. m2square + 4n 2square

Answer 1

To Find :

The squares of the following expressions :

1] 3x+5y

2] a+b

3] m²+4n²

Identity To Be Used :

• (a+b)² = a²+b²+2ab

Solution :

1] (3x+5y)²

So, using the identity:

(a+b)² = a²+b²+2ab,

here, a=3x

b = 5y

So, (3x+5y)²

= (3x)²+(5y)²+2(3x.5y)

= 9x²+25y²+30xy

Hence, (3x+5y)² = 9x²+25y²+3xy

_____________________

2] (a+b)²

So, using the identity :

(a+b)² = a²+b²+2ab

Here, a = a

b = b

So, (a+b)²

= a²+b²+2ab

_____________________

3] (m²+4n²)²

So, using the identity :

(a+b)² = a²+b²+2ab

a = m²

b = 4n²

So, (m²+4n²)²

= (m²)² + (4n²)² + 2(m².4n²)

= m⁴+16n⁴+2(2mn)²

= m⁴+16n⁴+8(mn)²

Hence, (m²+4n²)² = m⁴+16n⁴+8m²n²

_____________________

Additional Information:

These Are some identities useful for expressions:

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• (a+b+c)² = a²+b²+c²+2ab+2bc+2ca
• (a+b)³ = a³+b³+3a²b+3ab²
• (a-b)³ = a³+3ab²-3a²b-b³
• x²-y² = (x+y)(x-y)
• (x+a)(x+b) = x²+(a+b)x+ab