Question

find the product. \\((-2r + 5)(-8r + 5)\\) \\(10r^2 + 30r - 25\\) \\(16r^2 - 50r + 25\\) \\(16r^2 + 25\\) \\(16r^2 - 30r - 25\\)

Explanation:

Step1: Apply FOIL method (First terms)

Multiply first terms of each binomial:
$(-2r) \times (-8r) = 16r^2$

Step2: Apply FOIL method (Outer terms)

Multiply outer terms of the binomials:
$(-2r) \times 5 = -10r$

Step3: Apply FOIL method (Inner terms)

Multiply inner terms of the binomials:
$5 \times (-8r) = -40r$

Step4: Apply FOIL method (Last terms)

Multiply last terms of each binomial:
$5 \times 5 = 25$

Step5: Combine all terms

Sum the results from Steps 1-4:
$16r^2 -10r -40r +25$

Step6: Combine like terms

Add the linear terms:
$16r^2 + (-10r-40r) +25 = 16r^2 -50r +25$

Answer:

B. $16r^2 - 50r + 25$