Example Question - difference of squares rule
Here are examples of questions we've helped users solve.
Factoring a Difference of Squares
The expression given in the image is: 100 - 121x^2 This is a difference of squares since 100 and 121x^2 are both perfect squares. It can be factored using the difference of squares factoring rule: a^2 - b^2 = (a + b)(a - b) In this case: a^2 = 100, so a = 10 b^2 = 121x^2, so b = 11x Now let's apply the difference of squares: 100 - 121x^2 = (10)^2 - (11x)^2 = (10 + 11x)(10 - 11x) The factored form of the expression is: (10 + 11x)(10 - 11x)
Simplifying Rational Expression
To simplify the given expression, you should recognize that the numerator can be factored using the difference of squares rule, and the denominator appears to be already factored. Here is the step-by-step simplification: The given expression is \(\dfrac{x^2 - 16}{x^2 - 3x - 28}\). Factor the numerator which is a difference of squares: \(\dfrac{(x + 4)(x - 4)}{x^2 - 3x - 28}\). Now let's factor the denominator. To factor a quadratic trinomial, we look for two numbers that multiply to the constant term (-28) and add to the linear coefficient (-3). Those two numbers are -7 and +4. \(\dfrac{(x + 4)(x - 4)}{(x - 7)(x + 4)}\). Now, the \((x + 4)\) term is both in the numerator and the denominator, so they can be canceled out: \(\dfrac{x - 4}{x - 7}\). The expression is now simplified to: \(x - 4 \over x - 7\), which cannot be simplified further.
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