Determine if a Polynomial (x-8)(x^2-16x+64)

Math
(x-8)(x2-16x+64)
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify the expression.
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Expand (x-8)(x2-16x+64) by multiplying each term in the first expression by each term in the second expression.
x⋅x2+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
Simplify terms.
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Simplify each term.
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Multiply x by x2 by adding the exponents.
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Multiply x by x2.
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Raise x to the power of 1.
x1x2+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
Use the power rule aman=am+n to combine exponents.
x1+2+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
x1+2+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
Add 1 and 2.
x3+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
x3+x(-16x)+x⋅64-8×2-8(-16x)-8⋅64
Rewrite using the commutative property of multiplication.
x3-16x⋅x+x⋅64-8×2-8(-16x)-8⋅64
Multiply x by x by adding the exponents.
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Move x.
x3-16(x⋅x)+x⋅64-8×2-8(-16x)-8⋅64
Multiply x by x.
x3-16×2+x⋅64-8×2-8(-16x)-8⋅64
x3-16×2+x⋅64-8×2-8(-16x)-8⋅64
Move 64 to the left of x.
x3-16×2+64⋅x-8×2-8(-16x)-8⋅64
Multiply -16 by -8.
x3-16×2+64x-8×2+128x-8⋅64
Multiply -8 by 64.
x3-16×2+64x-8×2+128x-512
x3-16×2+64x-8×2+128x-512
Simplify by adding terms.
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Subtract 8×2 from -16×2.
x3-24×2+64x+128x-512
Add 64x and 128x.
x3-24×2+192x-512
x3-24×2+192x-512
x3-24×2+192x-512
x3-24×2+192x-512
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Polynomial
Determine if a Polynomial (x-8)(x^2-16x+64)

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