Question

16x^2-72xy+*, what can we put instead of * and can you please show me the explanation , please solve it

Answer 1

The factored form is
`(4x-9y)^2`

To factor the quadratic expression
`16x^2 -72xy+81y^2` , we can look for two binomials in the form

`(ax-by)^2` ,

where a and b are constants. The square of this binomial will have the desired quadratic expression.

Let's factor the given expression:

`16x^2 -72xy+81y^2`

This expression can be factored into the square of a binomial.

The binomial will have the form 4x−9y, since

`(4x-9y)^2 =16x^2 -72xy+81y^2 .`

So, the factored form is:

`(4x-9y)^2`

Alternatively, you can expand
`(4x-9y)^2` to verify that it equals the given expression.

Question

Factor the expression {eq}16x^2 - 72xy + 81y^2 {/eq} into a product of binomials.