Question

Find k so that 25x^2 + 40x + k is the square of the binomial.

Answer 1

k= 16

25x^2+40x+16x comes to be (5x+4)^2.

Answer 2

The value of k is, 16

Explanation:

Using the square of the binomial.

`(a+b)^2 = a^2+2ab+b^2` .....[1]

Given the polynomial

`25x^2+40x+k`

On comparing with [1] we have;

`a^2 = 25x^2`

`2ab = 40x` and

`b^2 = k`

then;

`a=√(25x^2) = 5x`

Solve for b:

`2ab =40x`

`2 \cdot 5x \cdot b =40x`

⇒
`10xb = 40x`

Divide both sides by 10x we have;

`b = 4`

it is given that:

`k = b^2 = 4^2 = 16`

then,

we get the square of the binomial;

`(5x+4)^2 = 25x^2+40x+16`

Therefore, the value of k is, 16