Question

1. simplify (collect like terms).

a) $-2z^2 + 3y - 10x - 4y + 4z^2 - 3z + 5y - 3z + 1$
b) $5x - 2y + 6 + \frac{5x - 2y + 6}{}$
c) $x + 4 - \frac{-x - 3}{}$
d) $x^2 - 5x + 3 - \frac{-2x^2 + 7x + 5}{}$
variable= $x$
constant= $4$
coefficient= $5$
solve and check:

Explanation:

Part a)

Step1: Identify like terms

Like terms: \( -2z^2 \) and \( 4z^2 \); \( 3y \), \( -4y \) and \( 5y \); \( -10x \); \( -3z \) and \( -3z \); constant \( 1 \)

Step2: Combine \( z^2 \) terms

\( -2z^2 + 4z^2 = 2z^2 \)

Step3: Combine \( y \) terms

\( 3y - 4y + 5y = 4y \)

Step4: Combine \( z \) terms

\( -3z - 3z = -6z \)

Step5: Combine remaining terms

\( 2z^2 + 4y - 10x - 6z + 1 \) (rearranged as \( -10x + 4y + 2z^2 - 6z + 1 \))

Step1: Identify like terms

Like terms: \( 5x \) and \( 5x \); \( -2y \) and \( -2y \); constants \( 6 \) and \( 6 \)

Step2: Combine \( x \) terms

\( 5x + 5x = 10x \)

Step3: Combine \( y \) terms

\( -2y - 2y = -4y \)

Step4: Combine constant terms

\( 6 + 6 = 12 \)

Step5: Combine all terms

\( 10x - 4y + 12 \)

Step1: Distribute the negative sign

\( x + 4 - (-x - 3) = x + 4 + x + 3 \) (since \( -(-x - 3)=x + 3 \))

Step2: Combine \( x \) terms

\( x + x = 2x \)

Step3: Combine constant terms

\( 4 + 3 = 7 \)

Step4: Combine all terms

\( 2x + 7 \)

Answer:

\( -10x + 4y + 2z^2 - 6z + 1 \)

Part b)