Question

Expand (x^22-3x^5 + x^-2 - 7) * (5x^4).

Can someone please explain in detail how to remove the parentheses step by step?

Answer 1

Let's see

`\\ \rm\Rrightarrow (x^(22)-3x^5+x^(-2)-7)5x^4`

Use distributive law

• a(b+c)=ab+ac

`\\ \rm\Rrightarrow 5x^(22+4)-15x^(5+4)+5x^(-2+4)-35x^4`

`\\ \rm\Rrightarrow 5x^(26)-15x^9+5x^2-35x^4`

Answer 2

`5x^(26)-15x^(9)+5x^(2)-35x^4`

Step-by-explanation:

Given expression:

`(x^(22)-3x^5 + x^(-2) - 7) (5x^4)`

Use the Distributive Property Law (b ± c)a = ab ± ac
to remove the parentheses:

`\implies 5x^4 \cdot x^(22)-5x^4 \cdot 3x^5+5x^4 \cdot x^(-2)-5x^4 \cdot 7`

Simplify by multiplying the coefficients of each term:

`\implies 5x^4 \cdot x^(22)-15x^4 \cdot x^5+5x^4 \cdot x^(-2)-35x^4`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c)`:

`\implies 5x^(4+22)-15x^(4+5)+5x^(4-2)-35x^4`

`\implies 5x^(26)-15x^(9)+5x^(2)-35x^4`