Answer:
(10 - 3x)(10 + 3x)
Step-by-step explanation:
This type of question yields what is called a difference of squares, which is recognizable because of the subtraction (-) operation between the two terms of the binomial. When questions like this are seen, the formula for difference of squares can be implemented. This formula is:
(a² - b²) = (a - b)(a + b)
With this, we can square root both terms of the original binomial and plug our variables for a and b into the formula.
Let 100 = a², let 9x² = b²
√(100) = 10
√(9x²) = 3x
Those values are now a and b, respectively, so when we place them in their spots in the formula, the completed factoring is: (10 - 3x)(10 + 3x)
To check this answer for accuracy, we can use the FOIL method and combine like terms to see if it gives us the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing us which terms should be multiplied together so:
Firsts: 10(10) = 100
Outsides: 10(3x) = 30x
Insides: -3x(10) = -30x
Lasts: -3x(3x) = -9x²
We place them in the same equation and combine like terms:
100 + 30x - 30x - 9x²
100 + 0 - 9x²
100 - 9x²
We are back to our original equation so the answer of (10 - 3x)(10 + 3x) is accurate.