Question

copy and simplify the following expressions by combining like terms.
a. (y + 2x-3 + 4x^{2}+3x - 5y)
b. (2x-6x^{2}+9 - 1-x - 3x)
c. (2y^{2}+30x-5y^{2}+4x - 4y - y)
d. (-10 + 3xy-3xy + y^{2}+10 - y^{2})

Explanation:

Step1: Combine like - terms for part a

Combine the $x^{2}$ terms, $x$ terms and $y$ terms separately.
$y + 2x-3 + 4x^{2}+3x - 5y=4x^{2}+(2x + 3x)+(y - 5y)-3=4x^{2}+5x-4y - 3$

Step2: Combine like - terms for part b

Combine the $x^{2}$ terms and $x$ terms.
$2x-6x^{2}+9 - 1-x - 3x=-6x^{2}+(2x - x-3x)+(9 - 1)=-6x^{2}-2x + 8$

Step3: Combine like - terms for part c

Combine the $x$ terms, $y^{2}$ terms and $y$ terms.
$2y^{2}+30x-5y^{2}+4x-4y - y=(2y^{2}-5y^{2})+(30x + 4x)+(-4y - y)=-3y^{2}+34x-5y$

Step4: Combine like - terms for part d

Combine the constant terms, $xy$ terms and $y^{2}$ terms.
$-10 + 3xy-3xy+y^{2}+10 - y^{2}=(-10 + 10)+(3xy-3xy)+(y^{2}-y^{2})=0$

Answer:

a. $4x^{2}+5x - 4y-3$
b. $-6x^{2}-2x + 8$
c. $-3y^{2}+34x-5y$
d. $0$