Question

assessment readiness

1. find the standard form for the product of \\((x^2 + 8)\\) and \\((x^2 - 2)\\). choose true or false for each statement about the product.

a. it is a \\(4^{\text{th}}\\) degree polynomial. \\(\circled{\text{true}}\\) \\(\bigcirc\\) false
b. the constant term is \\(-16\\). \\(\circled{\text{true}}\\) \\(\bigcirc\\) false
c. it has 3 terms. \\(\circled{\text{true}}\\) \\(\bigcirc\\) false

1. multiply \\((5x - 9)^2\\). choose true or false for each statement about the product.

a. the coefficient of the \\(x\\)-term is \\(-45\\). \\(\bigcirc\\) true \\(\circled{\text{false}}\\)
b. the leading term is \\(25x^2\\). \\(\circled{\text{true}}\\) \\(\bigcirc\\) false
c. the constant term is \\(81\\). \\(\circled{\text{true}}\\) \\(\bigcirc\\) false
find the product \\((3x + 6)(3x - 6)\\). show your work.
\\(\boxed{9x^2 - x - 36}\\) (crossed out) and handwritten \\((3x + 6)(3x - 6) \
ightarrow 9x^2 - 36\\)
find the product \\((x + 10)(4x + 5)\\). show your work.
handwritten: \\(x^2 + 5x + 40x + 50\\) (and \yes! you got it\ in red)

Explanation:

Question 3: Find the product \((3x + 6)(3x - 6)\)

Step1: Identify the formula

This is a difference of squares, which follows the formula \((a + b)(a - b) = a^2 - b^2\). Here, \(a = 3x\) and \(b = 6\).

Step2: Apply the formula

Substitute \(a = 3x\) and \(b = 6\) into the formula: \((3x)^2 - 6^2\).

Step3: Simplify each term

Calculate \((3x)^2 = 9x^2\) and \(6^2 = 36\). So the product is \(9x^2 - 36\).

Question (the one with \((x + 10)(4x + 5)\)): Find the product \((x + 10)(4x + 5)\)

Step1: Use the distributive property (FOIL method)

Multiply the First terms: \(x \times 4x = 4x^2\).
Multiply the Outer terms: \(x \times 5 = 5x\).
Multiply the Inner terms: \(10 \times 4x = 40x\).
Multiply the Last terms: \(10 \times 5 = 50\).

Step2: Combine like terms

Add the outer and inner terms: \(5x + 40x = 45x\).
Combine all terms: \(4x^2 + 45x + 50\).

Answer:

\(9x^2 - 36\)