Question

Subtract the product of $(x+y)(5x-y)$ from the product of $(3x+y)(x+5y)$.

• A. $2x^2+12xy+6y^2$
• B. $-2x^2+12xy+4y^2$
• C. $-2x^2+12xy+6y^2$
• D. $-2x^2-12xy-4y^2$

Answer 1

The correct option is C $-2x^2+12xy+6y^2$

Consider the first expression,$(x+y)(5x-y)=x(5x-y)+y(5x-y)$
$=5x^2-xy+5xy-y^2$
$=5x^2+4xy-y^2$-----(1)
Consider the second expression,
$(3x+y)(x+5y)=3x(x+5y)+y(x+5y)$
$=3x^2+15xy+xy+5y^2$
$=3x^2+16xy+5y^2$----(2)
Subtracting equation (1) from equation (2),
$=(3x^2+16xy+5y^2)$$-(5x^2+4xy-y^2)$
Grouping the like terms together,
$=(3x^2-5x^2)+(16xy-4xy)+(5y^2+y^2)$
$=-2x^2+12xy+6y^2$