Solve (x-3)^2(2x 1)^3 (x-3)^3(2x 1)^2 - ScanMath

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Question

Simplify the expression

32 x^{10} - 480 x^{9} + 2880 x^{8} - 8640 x^{7} + 12960 x^{6} - 7776 x^{5}

Evaluate

(x - 3)^{2} (2 x \times 1)^{3} (x - 3)^{3} (2 x \times 1)^{2}

Multiply the terms

(x - 3)^{2} (2 x)^{3} (x - 3)^{3} (2 x \times 1)^{2}

Multiply the terms

(x - 3)^{2} (2 x)^{3} (x - 3)^{3} (2 x)^{2}

Multiply the terms with the same base by adding their exponents

(x - 3)^{2 + 3} (2 x)^{3} (2 x)^{2}

Add the numbers

(x - 3)^{5} (2 x)^{3} (2 x)^{2}

Multiply the terms with the same base by adding their exponents

(x - 3)^{5} (2 x)^{3 + 2}

Add the numbers

(x - 3)^{5} (2 x)^{5}

Multiply the terms

(2 x (x - 3))^{5}

Evaluate the power

2^{5} x^{5} (x - 3)^{5}

Evaluate the power

32 x^{5} (x - 3)^{5}

Evaluate the power

32 x^{5} (x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243)

Apply the distributive property

32 x^{5} \times x^{5} - 32 x^{5} \times 15 x^{4} + 32 x^{5} \times 90 x^{3} - 32 x^{5} \times 270 x^{2} + 32 x^{5} \times 405 x - 32 x^{5} \times 243

Multiply the terms

More Steps

32 x^{10} - 32 x^{5} \times 15 x^{4} + 32 x^{5} \times 90 x^{3} - 32 x^{5} \times 270 x^{2} + 32 x^{5} \times 405 x - 32 x^{5} \times 243

Multiply the terms

More Steps

32 x^{10} - 480 x^{9} + 32 x^{5} \times 90 x^{3} - 32 x^{5} \times 270 x^{2} + 32 x^{5} \times 405 x - 32 x^{5} \times 243

Multiply the terms

More Steps

32 x^{10} - 480 x^{9} + 2880 x^{8} - 32 x^{5} \times 270 x^{2} + 32 x^{5} \times 405 x - 32 x^{5} \times 243

Multiply the terms

More Steps

32 x^{10} - 480 x^{9} + 2880 x^{8} - 8640 x^{7} + 32 x^{5} \times 405 x - 32 x^{5} \times 243

Multiply the terms

More Steps

32 x^{10} - 480 x^{9} + 2880 x^{8} - 8640 x^{7} + 12960 x^{6} - 32 x^{5} \times 243

Solution

32 x^{10} - 480 x^{9} + 2880 x^{8} - 8640 x^{7} + 12960 x^{6} - 7776 x^{5}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 3

Show Solution