Solve (x-7)*(x+7)*(x^2+49)

$$( x - 7 ) \cdot ( x + 7 ) \cdot ( x ^ { 2 } + 49 )$$

Evaluate

$$x^{4}-2401$$

Solution Steps

Use the distributive property to multiply x-7 by x+7 and combine like terms.

$$\left(x^{2}-49\right)\left(x^{2}+49\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 49.

$$\left(x^{2}\right)^{2}-2401$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-2401$$

Expand

$$x^{4}-2401$$

Solution Steps

Use the distributive property to multiply x-7 by x+7 and combine like terms.

$$\left(x^{2}-49\right)\left(x^{2}+49\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 49.

$$\left(x^{2}\right)^{2}-2401$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-2401$$