Solve (4 - b - c)^2 16b^2 16c^2

Question

Simplify the expression

4096 b^{2} c^{2} + 256 b^{4} c^{2} + 256 c^{4} b^{2} - 2048 b^{3} c^{2} - 2048 c^{3} b^{2} + 512 b^{3} c^{3}

Evaluate

(4 - b - c)^{2} \times 16 b^{2} \times 16 c^{2}

Multiply the terms

(4 - b - c)^{2} \times 256 b^{2} c^{2}

Use the commutative property to reorder the terms

256 (4 - b - c)^{2} b^{2} c^{2}

Evaluate the power

More Steps

256 (16 + b^{2} + c^{2} - 8 b - 8 c + 2 b c) b^{2} c^{2}

Multiply the terms

More Steps

(4096 + 256 b^{2} + 256 c^{2} - 2048 b - 2048 c + 512 b c) b^{2} c^{2}

Multiply the terms

More Steps

(4096 b^{2} + 256 b^{4} + 256 c^{2} b^{2} - 2048 b^{3} - 2048 c b^{2} + 512 b^{3} c) c^{2}

Apply the distributive property

4096 b^{2} c^{2} + 256 b^{4} c^{2} + 256 c^{2} b^{2} c^{2} - 2048 b^{3} c^{2} - 2048 c b^{2} c^{2} + 512 b^{3} c \times c^{2}

Multiply the terms

More Steps

4096 b^{2} c^{2} + 256 b^{4} c^{2} + 256 c^{4} b^{2} - 2048 b^{3} c^{2} - 2048 c b^{2} c^{2} + 512 b^{3} c \times c^{2}

Multiply the terms

More Steps

4096 b^{2} c^{2} + 256 b^{4} c^{2} + 256 c^{4} b^{2} - 2048 b^{3} c^{2} - 2048 c^{3} b^{2} + 512 b^{3} c \times c^{2}

Solution

More Steps

4096 b^{2} c^{2} + 256 b^{4} c^{2} + 256 c^{4} b^{2} - 2048 b^{3} c^{2} - 2048 c^{3} b^{2} + 512 b^{3} c^{3}

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