QuestionMultiply and simplify: $-2 x^{6}(5 x^{6}+3 x^{3}+7)$

Studdy Solution

STEP 1

Assumptions1. We are given the expression $- x^{6}\left(5 x^{6}+3 x^{3}+7\right)$ . We need to multiply and simplify this expression

STEP 2

We will use the distributive property, which states that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds true. In this case, we will distribute $-2 x^{6}$ to each term inside the parentheses.
$-2 x^{6} 5 x^{6} + -2 x^{6} * x^{} + -2 x^{6} *7$

STEP 3

Now, we will simplify each term. When multiplying terms with the same base, we add the exponents.
$-10 x^{12} + -6 x^{9} + -14 x^{6}$

STEP 4

Finally, we simplify the expression by combining like terms. In this case, there are no like terms, so the expression is already in its simplest form.
$-10 x^{12} -6 x^{9} -14 x^{6}$ This is the simplified form of the given expression.

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