Solve (x-2)^2 (2x-10)^2

Question

Simplify the expression

4 x^{4} - 56 x^{3} + 276 x^{2} - 560 x + 400

Evaluate

(x - 2)^{2} (2 x - 10)^{2}

Expand the expression

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(x^{2} - 4 x + 4) (2 x - 10)^{2}

Expand the expression

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(x^{2} - 4 x + 4) (4 x^{2} - 40 x + 100)

Apply the distributive property

x^{2} \times 4 x^{2} - x^{2} \times 40 x + x^{2} \times 100 - 4 x \times 4 x^{2} - (- 4 x \times 40 x) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the terms

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4 x^{4} - x^{2} \times 40 x + x^{2} \times 100 - 4 x \times 4 x^{2} - (- 4 x \times 40 x) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the terms

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4 x^{4} - 40 x^{3} + x^{2} \times 100 - 4 x \times 4 x^{2} - (- 4 x \times 40 x) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Use the commutative property to reorder the terms

4 x^{4} - 40 x^{3} + 100 x^{2} - 4 x \times 4 x^{2} - (- 4 x \times 40 x) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the terms

More Steps

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 4 x \times 40 x) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the terms

More Steps

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 160 x^{2}) - 4 x \times 100 + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the numbers

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 160 x^{2}) - 400 x + 4 \times 4 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the numbers

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 160 x^{2}) - 400 x + 16 x^{2} - 4 \times 40 x + 4 \times 100

Multiply the numbers

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 160 x^{2}) - 400 x + 16 x^{2} - 160 x + 4 \times 100

Multiply the numbers

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} - (- 160 x^{2}) - 400 x + 16 x^{2} - 160 x + 400

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

4 x^{4} - 40 x^{3} + 100 x^{2} - 16 x^{3} + 160 x^{2} - 400 x + 16 x^{2} - 160 x + 400

Subtract the terms

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4 x^{4} - 56 x^{3} + 100 x^{2} + 160 x^{2} - 400 x + 16 x^{2} - 160 x + 400

Add the terms

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4 x^{4} - 56 x^{3} + 276 x^{2} - 400 x - 160 x + 400

Solution

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4 x^{4} - 56 x^{3} + 276 x^{2} - 560 x + 400

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Factor the expression

4 (x - 2)^{2} (x - 5)^{2}

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Find the roots

x_{1} = 2, x_{2} = 5

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