Simplify (5-3 square root of -48)(2-4 square root of -27)

Math
(5-3-48)(2-4-27)
Rewrite -48 as -1(48).
(5-3-1(48))(2-4-27)
Rewrite -1(48) as -1⋅48.
(5-3(-1⋅48))(2-4-27)
Rewrite -1 as i.
(5-3(i⋅48))(2-4-27)
Rewrite -27 as -1(27).
(5-3(i⋅48))(2-4-1(27))
Rewrite -1(27) as -1⋅27.
(5-3(i⋅48))(2-4(-1⋅27))
Rewrite -1 as i.
(5-3(i⋅48))(2-4(i⋅27))
Simplify terms.
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Simplify each term.
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Rewrite 48 as 42⋅3.
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Factor 16 out of 48.
(5-3(i⋅16(3)))(2-4(i⋅27))
Rewrite 16 as 42.
(5-3(i⋅42⋅3))(2-4(i⋅27))
(5-3(i⋅42⋅3))(2-4(i⋅27))
Pull terms out from under the radical.
(5-3(i⋅(43)))(2-4(i⋅27))
Move 4 to the left of i.
(5-3(4⋅i3))(2-4(i⋅27))
Multiply 4 by -3.
(5-12i3)(2-4(i⋅27))
(5-12i3)(2-4(i⋅27))
Simplify each term.
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Rewrite 27 as 32⋅3.
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Factor 9 out of 27.
(5-12i3)(2-4(i⋅9(3)))
Rewrite 9 as 32.
(5-12i3)(2-4(i⋅32⋅3))
(5-12i3)(2-4(i⋅32⋅3))
Pull terms out from under the radical.
(5-12i3)(2-4(i⋅(33)))
Move 3 to the left of i.
(5-12i3)(2-4(3⋅i3))
Multiply 3 by -4.
(5-12i3)(2-12i3)
(5-12i3)(2-12i3)
(5-12i3)(2-12i3)
Expand (5-12i3)(2-12i3) using the FOIL Method.
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Apply the distributive property.
5(2-12i3)-12i3(2-12i3)
Apply the distributive property.
5⋅2+5(-12i3)-12i3(2-12i3)
Apply the distributive property.
5⋅2+5(-12i3)-12i3⋅2-12i3(-12i3)
5⋅2+5(-12i3)-12i3⋅2-12i3(-12i3)
Simplify and combine like terms.
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Simplify each term.
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Multiply 5 by 2.
10+5(-12i3)-12i3⋅2-12i3(-12i3)
Multiply -12 by 5.
10-60(i3)-12i3⋅2-12i3(-12i3)
Multiply 2 by -12.
10-60i3-24i3-12i3(-12i3)
Multiply -12i3(-12i3).
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Multiply -12 by -12.
10-60i3-24i3+144i3(i3)
Raise i to the power of 1.
10-60i3-24i3+144(i1i)33
Raise i to the power of 1.
10-60i3-24i3+144(i1i1)33
Use the power rule aman=am+n to combine exponents.
10-60i3-24i3+144i1+133
Add 1 and 1.
10-60i3-24i3+144i233
Raise 3 to the power of 1.
10-60i3-24i3+144i2(313)
Raise 3 to the power of 1.
10-60i3-24i3+144i2(3131)
Use the power rule aman=am+n to combine exponents.
10-60i3-24i3+144i231+1
Add 1 and 1.
10-60i3-24i3+144i232
10-60i3-24i3+144i232
Rewrite i2 as -1.
10-60i3-24i3+144⋅-132
Multiply 144 by -1.
10-60i3-24i3-14432
Rewrite 32 as 3.
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Use axn=axn to rewrite 3 as 312.
10-60i3-24i3-144(312)2
Apply the power rule and multiply exponents, (am)n=amn.
10-60i3-24i3-144⋅312⋅2
Combine 12 and 2.
10-60i3-24i3-144⋅322
Cancel the common factor of 2.
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Cancel the common factor.
10-60i3-24i3-144⋅322
Divide 1 by 1.
10-60i3-24i3-144⋅31
10-60i3-24i3-144⋅31
Evaluate the exponent.
10-60i3-24i3-144⋅3
10-60i3-24i3-144⋅3
Multiply -144 by 3.
10-60i3-24i3-432
10-60i3-24i3-432
Subtract 432 from 10.
-60i3-24i3-422
Subtract 24i3 from -60i3.
-84i3-422
-84i3-422
Reorder -84i3 and -422.
-422-84i3
Simplify (5-3 square root of -48)(2-4 square root of -27)

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