Answer:
First, draw a rectangle and draw 3 lines going vertically. Then, draw the diagonal lines (shown in step 3) write the 4 digit number you are multiplying with the 1 digit number on top of the table (step 2) and multiply, when you are done multiplying, add the numbers vertically. Finally, you have your answer
Step-by-step explanation:
(3x2 + 9x + 6) − (8x2 + 3x − 10) + (2x + 4)(3x − 7)
First distribute the (2x+4)(3x-7) to get 6x2-2x-28
After this just add the like terms for all parts of the expression.
(3x2-8x2+6x2)+(9x-3x-2x)+(6+10-28)
x2+4x-12
So you answer is x2+4x-12
Answer: a²+b² = -99/2
Step-by-step explanation:
Since we are given two equations, this equations will be solved simultaneously to get a² and b²
a³ - 3ab² = 47 ... 1
b³ - 3a² b = 52... 2
From 1, a(a² - 3b²) = 47...3
From 2, b(b² - 3a²) = 52... 4
Adding 3 and 4, we have;
a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)
a²+b²-(3b²+3a²) = 99
(a²+b²) -3(b²+a²)= 99
Taking the difference we have
- 2(a²+b²) = 99
a²+b² = -99/2
![\boxed{\underline{\bf \: ANSWER}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cunderline%7B%5Cbf%20%5C%3A%20ANSWER%7D%7D)
![\sf \: ( 5 + 6 i ) ( 5 - 6 i )](https://tex.z-dn.net/?f=%20%5Csf%20%5C%3A%20%28%205%20%2B%206%20i%20%29%20%28%205%20-%206%20i%20%29)
Multiply complex numbers 5+6i and 5-6i in the same way as you multiply binomials.
![\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)i^{2}](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%205%5Ctimes%205%2B5%5Ctimes%20%5Cleft%28-6i%5Cright%29%2B6i%5Ctimes%205%2B6%5Cleft%28-6%5Cright%29i%5E%7B2%7D%20)
By definition, i² is -1.
![\dashrightarrow \sf 5\times 5+5\times \left(-6i\right)+6i\times 5+6\left(-6\right)\left(-1\right)](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%205%5Ctimes%205%2B5%5Ctimes%20%5Cleft%28-6i%5Cright%29%2B6i%5Ctimes%205%2B6%5Cleft%28-6%5Cright%29%5Cleft%28-1%5Cright%29%20)
Do the multiplications.
![\dashrightarrow \sf \: 25-30i+30i+36](https://tex.z-dn.net/?f=%20%5Cdashrightarrow%20%5Csf%20%5C%3A%2025-30i%2B30i%2B36%20)
Now cancel -30i & +30i
![\dashrightarrow \sf \: 25 \: \bcancel{- 30i} \: + \: \bcancel{30i}+36](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20%5C%3A%2025%20%5C%3A%20%20%5Cbcancel%7B-%2030i%7D%20%20%5C%3A%20%20%2B%20%20%5C%3A%20%5Cbcancel%7B30i%7D%2B36%20)
Now the equation becomes
![\dashrightarrow \sf \: 25 \: + 36 \\ \dashrightarrow \boxed{\bf \: 61}](https://tex.z-dn.net/?f=%5Cdashrightarrow%20%5Csf%20%5C%3A%2025%20%5C%3A%20%20%2B%2036%20%5C%5C%20%5Cdashrightarrow%20%20%5Cboxed%7B%5Cbf%20%5C%3A%2061%7D)
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Hope it helps.
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