Given:
The expression is [tex](x+4y)^2[/tex].
The expression [tex]ax(2x+y-5)[/tex] simplifies to [tex]6x^2+3xy-15x[/tex].
To find:
The equivalent expression.
The value of a.
Solution:
The expression is
[tex](x+4y)^2[/tex]
Using [tex](a+b)^2=a^2+2ab+b^2[/tex], we get
[tex](x+4y)^2=x^2+2(x)(4y)+(4y)^2[/tex]
[tex](x+4y)^2=x^2+8xy+16y^2[/tex]
Therefore, the correct option is A.
The expression [tex]ax(2x+y-5)[/tex] simplifies to [tex]6x^2+3xy-15x[/tex]. So,
[tex]ax(2x+y-5)=6x^2+3xy-15x[/tex]
[tex]2ax^2+axy-5ax=6x^2+3xy-15x[/tex]
On comparing the coefficient of [tex]x^2[/tex],, we get
[tex]2a=6[/tex]
Divide both sides by 2.
[tex]a=3[/tex]
Therefore, the value of a is 3.