Expand and simplify the trigonometric expression 8(sec(x)^2-1)(sec(x)-1)

 Exercise

$8\left(sec^2x-1\right)\left(secx-1\right)$

 

Multiply the single term $8\left(\sec\left(x\right)-1\right)$ by each term of the polynomial $\left(\sec\left(x\right)^2-1\right)$

$8\sec\left(x\right)^2\left(\sec\left(x\right)-1\right)-8\left(\sec\left(x\right)-1\right)$

 

Multiply the single term $8\sec\left(x\right)^2$ by each term of the polynomial $\left(\sec\left(x\right)-1\right)$

$8\sec\left(x\right)\sec\left(x\right)^2-8\sec\left(x\right)^2-8\left(\sec\left(x\right)-1\right)$

 

When multiplying exponents with same base you can add the exponents: $8\sec\left(x\right)\sec\left(x\right)^2$

$8\sec\left(x\right)^{3}-8\sec\left(x\right)^2-8\left(\sec\left(x\right)-1\right)$

 

Multiply the single term $-8$ by each term of the polynomial $\left(\sec\left(x\right)-1\right)$

$8\sec\left(x\right)^{3}-8\sec\left(x\right)^2-8\sec\left(x\right)+8$

$8\sec\left(x\right)^{3}-8\sec\left(x\right)^2-8\sec\left(x\right)+8$

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