Question

question 4

subtract the following multivariable polynomials:
\\((3a^2 - 2ab^2 + 5b^2) - (2a^2 + 5ab^2 + 2b^2)\\)

• \\(a^2 - 7ab^2 + 3b^2\\)
• \\(a^2 - 3ab^2 + 3b^2\\)
• \\(a^2 + 3ab^2 + 7b^2\\)
• \\(a^2 + 3ab^2 + 3b^2\\)

question 5

multiply the following multivariable polynomials:
\\((3x + 2y)(2x + 5y)\\)

• \\(6x^2 + 19xy + 10y^2\\)
• \\(6x^2 + 15xy + 10y^2\\)
• \\(60x^2y^2 + 19x\\)
• \\(6x^2 + 10y^2\\)

Explanation:

Distribute the negative sign

Using the Distributive Property with Negative Sign knowledge point

$$
LATEXBLOCK0
$$

Combine the like terms

Using the Combining Like Terms and Polynomial Subtraction knowledge points

$$
LATEXBLOCK1
$$

Multiply the binomials

We multiply the terms of the two binomials using the FOIL method:

$$
LATEXBLOCK2
$$

Combine the middle terms

We combine the like terms containing \(xy\) to simplify the expression:

$$
LATEXBLOCK3
$$

Answer:

Question 4

• (A) \(a^2 - 7ab^2 + 3b^2\) (Correct answer)
• (B) \(a^2 - 3ab^2 + 3b^2\)
• (C) \(a^2 + 3ab^2 + 7b^2\)
• (D) \(a^2 + 3ab^2 + 3b^2\)

Question 5

• (A) \(6x^2 + 19xy + 10y^2\) (Correct answer)
• (B) \(6x^2 + 15xy + 10y^2\)
• (C) \(60x^2y^2 + 19x\)
• (D) \(6x^2 + 10y^2\)