Question

Which of the following expressions are equivalent to (x+4y)^2 check all that apply: A. x^2+8xy+16y^2 B. x^2+2xy+2y(x+2y) C. x^2+16y^2 D. x^2+4xy+4y(x+4y) Question 2. If the expression ax(2x+y-5) simplifies to 6x^2+3xy-15x, what is the value of a? Type only the numeric value into the box.

Answer 1

Given:

The expression is
`(x+4y)^2`.

The expression
`ax(2x+y-5)` simplifies to
`6x^2+3xy-15x`.

To find:

The equivalent expression.

The value of a.

Solution:

The expression is

`(x+4y)^2`

Using
`(a+b)^2=a^2+2ab+b^2`, we get

`(x+4y)^2=x^2+2(x)(4y)+(4y)^2`

`(x+4y)^2=x^2+8xy+16y^2`

Therefore, the correct option is A.

The expression
`ax(2x+y-5)` simplifies to
`6x^2+3xy-15x`. So,

`ax(2x+y-5)=6x^2+3xy-15x`

`2ax^2+axy-5ax=6x^2+3xy-15x`

On comparing the coefficient of
`x^2`,, we get

`2a=6`

Divide both sides by 2.

`a=3`

Therefore, the value of a is 3.