Explain the. different ways that u can use multiplication to estimate. and solve. division problems

Instead of divide the dividend by the divisor to get a quotient, you can estimate an approximate quotient and then multiply it by the dividend. If the result is greater than the divisor, then your estimated quotient was greater than the actual quotient, in the case that the result is lower than the divisor, then your estimated quotient was lower than the actual quotient. After that you proceed to estimate again the quotient. For example:

First approximation:

192/12 ≈ 14

12*14 = 168 < 192

Second approximation:

192/12 ≈ 20

12*20 = 240

So, the answer is between 14 and 20

Third approximation:

192/12 ≈ 16

12*16 = 192

Then, 16 is the correct answer

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81