Solve (a-2)(a-4)(a-6)(a-8) 16

Question

Simplify the expression

16 a^{4} - 320 a^{3} + 2240 a^{2} - 6400 a + 6144

Evaluate

(a - 2) (a - 4) (a - 6) (a - 8) \times 16

Use the commutative property to reorder the terms

16 (a - 2) (a - 4) (a - 6) (a - 8)

Multiply the terms

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(16 a - 32) (a - 4) (a - 6) (a - 8)

Multiply the terms

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(16 a^{2} - 96 a + 128) (a - 6) (a - 8)

Multiply the terms

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(16 a^{3} - 192 a^{2} + 704 a - 768) (a - 8)

Apply the distributive property

16 a^{3} \times a - 16 a^{3} \times 8 - 192 a^{2} \times a - (- 192 a^{2} \times 8) + 704 a \times a - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the terms

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16 a^{4} - 16 a^{3} \times 8 - 192 a^{2} \times a - (- 192 a^{2} \times 8) + 704 a \times a - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the numbers

16 a^{4} - 128 a^{3} - 192 a^{2} \times a - (- 192 a^{2} \times 8) + 704 a \times a - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the terms

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16 a^{4} - 128 a^{3} - 192 a^{3} - (- 192 a^{2} \times 8) + 704 a \times a - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the numbers

16 a^{4} - 128 a^{3} - 192 a^{3} - (- 1536 a^{2}) + 704 a \times a - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the terms

16 a^{4} - 128 a^{3} - 192 a^{3} - (- 1536 a^{2}) + 704 a^{2} - 704 a \times 8 - 768 a - (- 768 \times 8)

Multiply the numbers

16 a^{4} - 128 a^{3} - 192 a^{3} - (- 1536 a^{2}) + 704 a^{2} - 5632 a - 768 a - (- 768 \times 8)

Multiply the numbers

16 a^{4} - 128 a^{3} - 192 a^{3} - (- 1536 a^{2}) + 704 a^{2} - 5632 a - 768 a - (- 6144)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

16 a^{4} - 128 a^{3} - 192 a^{3} + 1536 a^{2} + 704 a^{2} - 5632 a - 768 a + 6144

Subtract the terms

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16 a^{4} - 320 a^{3} + 1536 a^{2} + 704 a^{2} - 5632 a - 768 a + 6144

Add the terms

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16 a^{4} - 320 a^{3} + 2240 a^{2} - 5632 a - 768 a + 6144

Solution

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16 a^{4} - 320 a^{3} + 2240 a^{2} - 6400 a + 6144

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Find the roots

a_{1} = 2, a_{2} = 4, a_{3} = 6, a_{4} = 8

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