Factor completely. 640-10x^(2)=

Identify common factor: Identify the common factor in the terms 640 and 10x^2. Both terms are divisible by 10.Factor out GCF: Factor out the greatest common factor (GCF) from 640 - 10x^2. 640 - 10x^2 = 10(64 - x^2)Recognize difference of squares: Recognize that 64 - x^2 is a difference of squares. 64 = 8^2 and x^2 = (x)^2, so 64 - x^2 can be written as 8^2 - x^2.Apply difference of squares formula: Apply the difference of squares formula to factor 64 - x^2. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). 8^2 - x^2 = (8 - x)(8 + x)Combine factored form with GCF: Combine the factored form of 64 - x^2 with the GCF factored out in Step 2. 10(64 - x^2) = 10(8 - x)(8 + x)

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

\newline

640-10x^{2}=

Identify common factor: Identify the common factor in the terms $640$ and $10x^2$ . $\newline$ Both terms are divisible by $10$ .
Factor out GCF: Factor out the greatest common factor (GCF) from $640 - 10x^2$ . $\newline$ $640 - 10x^2 = 10(64 - x^2)$
Recognize difference of squares: Recognize that $64 - x^2$ is a difference of squares. $\newline$ $64 = 8^2$ and $x^2 = (x)^2$ , so $64 - x^2$ can be written as $8^2 - x^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor $64 - x^2$ . $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . $\newline$ $8^2 - x^2 = (8 - x)(8 + x)$
Combine factored form with GCF: Combine the factored form of $64 - x^2$ with the GCF factored out in Step $2$ . $\newline$ $10(64 - x^2) = 10(8 - x)(8 + x)$