Expand the expression (x^(a+x)-3x^(a-2))^2

 Exercise

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

 

Expand $\left(x^{\left(a+x\right)}-3x^{\left(a-2\right)}\right)^2$

$x^{2\left(a+x\right)}-6x^{\left(a+x\right)}x^{\left(a-2\right)}+\left(-3x^{\left(a-2\right)}\right)^2$

 

When multiplying exponents with same base we can add the exponents

$x^{2\left(a+x\right)}-6x^{\left(a+x+a-2\right)}+\left(-3x^{\left(a-2\right)}\right)^2$

 

Combining like terms $a$ and $a$

$x^{2\left(a+x\right)}-6x^{\left(2a+x-2\right)}+\left(-3x^{\left(a-2\right)}\right)^2$

 

Multiply the single term $2$ by each term of the polynomial $\left(a+x\right)$

$x^{\left(2a+2x\right)}-6x^{\left(2a+x-2\right)}+\left(-3x^{\left(a-2\right)}\right)^2$

$x^{\left(2a+2x\right)}-6x^{\left(2a+x-2\right)}+\left(-3x^{\left(a-2\right)}\right)^2$

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