Question

Expand (2p + 3m + 4n)² slove the question ​

Answer 1

Answer:

4p^2+9m^2+16n^2+12pm+24mn+16np

Step-by-step explanation:

(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca

(2p + 3m + 4n)²=(2p)^2+(3m)^2+(4n)^2+2(2p)(3m)+2(3m)(4n)+2(4n)(2p)

=4p^2+9m^2+16n^2+12pm+24mn+16np

Answer 2

Given: (2p + 3m + 4n)²

To find: The expansion of the expression

Solution: The given expression is in the form of (a + b + c)² where a = 2p, b = 3m and c = 4n.

And we know that (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Therefore expanding the expression in this form,

(2p + 3m + 4n)²

= (2p)² + (3m)² + (4n)² + 2(2p × 3m + 3m × 4n + 4n × 2p)

= 4p² + 9m² + 16n² + 2(6pm + 12mn + 8np)

= 4p² + 9m² + 16n² + 12pm + 24mn + 16np

Answer: 4p² + 9m² + 16n² + 12pm + 24mn + 16np