Question

Express 9x²+24xy+16y²

as the product of two same

expressions​

Answer 1

Answer:

3x+4y

Step-by-step explanation:

9x^2+24xy+16y^2

let we split 24 into 2

9x^2+12xy+12xy+16y^2

3x(3x+4y)+4y(3x+4y)

(3x+4y)(3x+4y)

3x+4y is the crt answer

Answer 2

Answer:

$(3x + 4y)^2$

Step-by-step explanation:

Given Question:

Express 9x²+24xy+16y² as the product of two same expressions​.

The question is rephrased. It basically means to represent it as the square of an expression.

Look at the first number of the given expression.

9x²

You can also express it as $(3x)^2 \:\:\: [3^2 = 9 \:\: and \:\: (x)^2 = x^2]$

Ignore the middle number of the expression, i.e., 24xy, for now.

Now, look at the 3rd number of the expression.

16y²

This can also be expressed as $(4y)^2 \:\:\: [4^2 = 16 \:\: and \:\: (y)^2 = y^2]$

Now, the expression can be rewritten as

$(3x)^2 + 24xy + (4y)^2$

Consider the 2nd term of the expression, i.e., 24xy, now.

This can be written as (2)(3x)(4y) by trial and error.

Now, we can write the expression as

$(3x)^2 + 2(3x)(4y) + (4y)^2$

Look at the expression closely.

It is in the form:

$a^2 + 2ab + b^2$, where a = 3x and b = 4y.

Hence, the expression can finally be written as

$(3x + 4y)^2$, since we are following the identity $(a + b)^2$= $a^2 + 2ab + b^2$,