Factor the expression completely. 90-10x^(3) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. The terms 90 and -10x^3 both have a common factor of 10. We can factor out the 10 from both terms.Factor out GCF: Factor out the GCF from the expression. The expression 90 - 10x^3 can be written as 10(9 - x^3) after factoring out the 10.Recognize difference of cubes: Recognize that the expression inside the parentheses is a difference of cubes. The expression 9 - x^3 can be factored further because it is a difference of cubes. The difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a is 3 and b is x, because 9 is 3^3 and x^3 is x^3.Apply cubes formula: Apply the difference of cubes formula to factor the expression inside the parentheses. Using the formula, we get (3 - x)(3^2 + 3x + x^2), which simplifies to (3 - x)(9 + 3x + x^2).Combine factored expressions: Combine the factored expression inside the parentheses with the GCF we factored out earlier. The completely factored form of the expression is 10(3 - x)(9 + 3x + x^2).

Home

Math Problems

Grade 7

Evaluate numerical expressions involving exponents

Full solution

Q. Factor the expression completely.

\newline

90-10 x^{3}

\newline

Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the expression. $\newline$ The terms $90$ and $-10x^3$ both have a common factor of $10$ . We can factor out the $10$ from both terms.
Factor out GCF: Factor out the GCF from the expression. $\newline$ The expression $90 - 10x^3$ can be written as $10(9 - x^3)$ after factoring out the $10$ .
Recognize difference of cubes: Recognize that the expression inside the parentheses is a difference of cubes. $\newline$ The expression $9 - x^3$ can be factored further because it is a difference of cubes. The difference of cubes formula is $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ . $\newline$ In this case, $a$ is $3$ and $b$ is $x$ , because $9$ is $3^3$ and $x^3$ is $x^3$ .
Apply cubes formula: Apply the difference of cubes formula to factor the expression inside the parentheses. $\newline$ Using the formula, we get $(3 - x)(3^2 + 3x + x^2)$ , which simplifies to $(3 - x)(9 + 3x + x^2)$ .
Combine factored expressions: Combine the factored expression inside the parentheses with the GCF we factored out earlier. $\newline$ The completely factored form of the expression is $10(3 - x)(9 + 3x + x^2)$ .