Question

a. line s b. line q c. line p d.
5: polynomials

1. subtract: $(3x - 7x^2 + 2) - (4x^2 - 5 + 6x)$

a. $-11x^2 + 3x - 7$ b. $-11x^2 - 9x - 3$ c. $-11x^2 - 3x + 7$ d. $11x^2 + 3x - 7$

1. subtract: $(3y^2 - 5x^2 + 4) - (2x - 8 + 4y^2)$

a. $-1y^2 - 5x^2 - 2x - 4$ b. $3y^2 - 7x^2 + 12$ c. $-4x + 12$ d. $-1y^2 - 5x^2 - 2x + 12$
questions i should practice:

Explanation:

Question 12

Step1: Distribute the negative sign

We have \((3x - 7x^{2}+2)-(4x^{2}-5 + 6x)\). Distribute the negative sign to the terms inside the second parentheses: \(3x - 7x^{2}+2-4x^{2}+5 - 6x\).

Step2: Combine like terms for \(x^{2}\) terms

The \(x^{2}\) terms are \(-7x^{2}\) and \(-4x^{2}\). Combining them: \(-7x^{2}-4x^{2}=-11x^{2}\).

Step3: Combine like terms for \(x\) terms

The \(x\) terms are \(3x\) and \(-6x\). Combining them: \(3x - 6x=-3x\).

Step4: Combine like terms for constant terms

The constant terms are \(2\) and \(5\). Combining them: \(2 + 5 = 7\).

Step5: Write the final polynomial

Putting it all together, we get \(-11x^{2}-3x + 7\).

Step1: Distribute the negative sign

We have \((3y^{2}-5x^{2}+4)-(2x - 8 + 4y^{2})\). Distribute the negative sign to the terms inside the second parentheses: \(3y^{2}-5x^{2}+4-2x + 8-4y^{2}\).

Step2: Combine like terms for \(y^{2}\) terms

The \(y^{2}\) terms are \(3y^{2}\) and \(-4y^{2}\). Combining them: \(3y^{2}-4y^{2}=-y^{2}\) (or \(-1y^{2}\)).

Step3: Combine like terms for \(x^{2}\) terms

The \(x^{2}\) term is \(-5x^{2}\) (no other \(x^{2}\) terms to combine with).

Step4: Combine like terms for \(x\) terms

The \(x\) term is \(-2x\) (no other \(x\) terms to combine with).

Step5: Combine like terms for constant terms

The constant terms are \(4\) and \(8\). Combining them: \(4 + 8 = 12\).

Step6: Write the final polynomial

Putting it all together, we get \(-y^{2}-5x^{2}-2x + 12\) (or \(-1y^{2}-5x^{2}-2x + 12\)).

Answer:

c. \(-11x^{2}-3x + 7\)

Question 13