Question

Find a value for m and n to make a true statement:
(mx+ny)²=4x²+12xy+9y²

Answer 1

• m = 2
• n = 3

Explanation:

To find:-

• The value of m and n for which the given statement is true.

Answer:-

We are given a equation,

`\longrightarrow (mx+ny)^2 = 4x^2+12xy+9y^2  \\`

Consider the LHS ,

`\longrightarrow (mx+ny)^2 \\`

We can expand it using an indentity ,

Identity:-

`\longrightarrow \boxed{ (a+b)^2=a^2+b^2+2ab}\\`

So we have;

`\longrightarrow (mx)^2+(ny)^2+2(mx)(ny) = 4x^2+12xy + 9y^2  \\`

Simplify,

`\longrightarrow  m^2(x^2) + n^2(y^2) + 2xy(mn) = 4x^2+12xy + 9y^2\\`

On comparing the respective terms , we have;

• 
  `\longrightarrow m^2 = 4  \\`
• 
  `\longrightarrow n^2 = 9  \\`

Simplify and solve for m and n as ,

`\longrightarrow m =√(4) =\boxed{2}\\`

`\longrightarrow n =√(9) =\boxed{3} \\`

Hence the value of m is 2 and that of n is 3 .

Answer 2

Answer: (2x + 3y)^2; m = 2 n = 3

Explanation:

another way to write (2x + 3y)^2 is

(2x+3y) (2x+3y) if you FOIL (First, Outsides, Insides, Lasts) you will get

4x^2 + 6xy + 6xy + 9y^2

= 4x^2 + 12xy + 9y^2