Question

Simplify the polynomial, then evaluate for x = 1 and y = –2.

a) (2xy + 3xy^2 – 3xy + 4xy – 5xy^2)

b) (bx^2y – xy^2 – 3xy – 14)

c) (bx^2y – 2xy – 3xy + y^2 – 10)

d) (bx^2y – xy^2 – 3xy – 10)

e) (bxy - 2xy – 3xy + y – 2)

Answer 1

To simplify the given polynomials, combine like terms. Then, substitute x = 1 and y = -2 to evaluate the expressions.

Step-by-step explanation:

To simplify the polynomial, we can combine like terms. Let's evaluate each expression:

a) (2xy + 3xy^2 – 3xy + 4xy – 5xy^2) = (2xy + 4xy) + (3xy^2 - 5xy^2) - 3xy = 6xy - 2xy^2 - 3xy = 3xy - 2xy^2

b) (bx^2y – xy^2 – 3xy – 14) = bx^2y - xy^2 - 3xy - 14

c) (bx^2y – 2xy – 3xy + y^2 – 10) = bx^2y - 5xy + y^2 - 10

d) (bx^2y – xy^2 – 3xy – 10) = bx^2y - xy^2 - 3xy - 10

e) (bxy - 2xy – 3xy + y – 2) = bxy - 5xy + y - 2

To evaluate for x = 1 and y = -2, substitute these values into the simplified expressions:

a) (3xy - 2xy^2) = 3(1)(-2) - 2(1)(-2)^2 = -6 + 8 = 2

b) (bx^2y - xy^2 - 3xy - 14) = b(1)^2(-2) - (1)(-2)^2 - 3(1)(-2) - 14 = -2b + 4 + 6 - 14 = -2b - 4

c) (bx^2y - 5xy + y^2 - 10) = b(1)^2(-2) - 5(1)(-2) + (-2)^2 - 10 = -2b + 10 + 4 - 10 = -2b + 4

d) (bx^2y - xy^2 - 3xy - 10) = b(1)^2(-2) - (1)(-2)^2 - 3(1)(-2) - 10 = -2b + 4 + 6 - 10 = -2b

e) (bxy - 5xy + y - 2) = b(1)(-2) - 5(1)(-2) + (-2) - 2 = -2b + 10 - 2 - 2 = -2b + 6