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

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

User Zrii
by
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2 Answers

9 votes

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

User Vikas Tawniya
by
7.4k points
3 votes

Answer:


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

User Terbubbs
by
8.2k points

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