What is (x+7)(x^2-7x+49)+(x^2+7x+49)(x-7) ?

The solution to (x+7)(x^2-7x+49)+(x^2+7x+49)(x-7) is 2x^3

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simplify (x+7)(x^2-7x+49)+(x^2+7x+49)(x-7)

simplify

(x + 7) (x^{2} - 7 x + 49) + (x^{2} + 7 x + 49) (x - 7)

2 x^{3}

Solution steps

(x + 7) (x^{2} - 7 x + 49) + (x^{2} + 7 x + 49) (x - 7)

Expand

(x + 7) (x^{2} - 7 x + 49) : x^{3} + 343

= x^{3} + 343 + (x^{2} + 7 x + 49) (x - 7)

Expand

(x^{2} + 7 x + 49) (x - 7) : x^{3} - 343

= x^{3} + 343 + x^{3} - 343

Group like terms

= x^{3} + x^{3} + 343 - 343

Add similar elements:

x^{3} + x^{3} = 2 x^{3}

= 2 x^{3} + 343 - 343

Subtract the numbers:

343 - 343 = 0

= 2 x^{3}

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What is (x+7)(x^2-7x+49)+(x^2+7x+49)(x-7) ?
The solution to (x+7)(x^2-7x+49)+(x^2+7x+49)(x-7) is 2x^3