1. Select all the expressions that are equivalent to 12x^3y^8 A. (2xy)(6x^2y^5)(y) B (-2xy)^2(3xy)(y^5) C. -(2^2x^2y^2)(3xy)(y^5) D. (2xy)^2(3xy^6) E -(2xy)(-3xy)^2(2y^5)

To determine which expressions are equivalent to $12x^{3}y}$, we need to simplify each expression and compare it with the given expression.<br /><br />A. $(2xy)(6x^{2}y^{5})(y)$<br /> Simplifying this expression:<br /> $(2xy)(6x^{2}y^{5})(y) = 12x^{3}y^{7}$<br /> This expression is not equivalent to $12x^{3}y^{8}$.<br /><br />B. $(-2xy)^{2}(3xy)(y^{5})$<br /> Simplifying this expression:<br /> $(-2xy)^{2}(3xy)(y^{5}) = 4x^{2}y^{2}(3xy)(y^{5}) = 12x^{3}y^{8}$<br /> This expression is equivalent to $12x^{3}y^{8}$.<br /><br />C. $-(2^{2}x^{2}y^{2})(3xy)(y^{5})$<br /> Simplifying this expression:<br /> $-(2^{2}x^{2}y^{2})(3xy)(y^{5}) = -4x^{2}y^{2}(3xy)(y^{5}) = -12x^{3}y^{8}$<br /> This expression is not equivalent to $12x^{3}y^{8}$.<br /><br />D. $(2xy)^{2}(3xy^{6})$<br /> Simplifying this expression:<br /> $(2xy)^{2}(3xy^{6}) = 4x^{2}y^{2}(3xy^{6}) = 12x^{3}y^{8}$<br /> This expression is equivalent to $12x^{3}y^{8}$.<br /><br />E. $-(2xy)(-3xy)^{2}(2y^{5})$<br /> Simplifying this expression:<br /> $-(2xy)(-3xy)^{2}(2y^{5}) = -(2xy)(9x^{2}y^{2})(2y^{5}) = -36x^{3}y^{9}$<br /> This expression is not equivalent to $12x^{3}y^{8}$.<br /><br />Therefore, the expressions that are equivalent to $12x^{3}y^{8}$ are B and D.