Question

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

Answer 1

Answer:

The value of k is, 16

Step-by-step 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;

$a=\sqrt{25x^2} = 5x$

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

Answer 2

K= 16

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