What is $g^2-36$ in factored form?
Answer (2)
Recognize the expression as a difference of squares: g 2 − 36 = g 2 − 6 2 .
Apply the difference of squares factorization formula: a 2 − b 2 = ( a − b ) ( a + b ) .
Substitute a = g and b = 6 into the formula: ( g − 6 ) ( g + 6 ) .
The factored form of the expression is ( g − 6 ) ( g + 6 ) .
Explanation
Recognizing the Pattern We are asked to factor the expression g 2 − 36 . This looks like a difference of squares, which has a specific factoring pattern.
Applying the Difference of Squares Formula The expression g 2 − 36 can be written as g 2 − 6 2 , which is a difference of squares. The difference of squares factorization formula is a 2 − b 2 = ( a − b ) ( a + b ) .
Factoring the Expression In our case, a = g and b = 6 . Substituting these values into the formula, we get g 2 − 36 = ( g − 6 ) ( g + 6 ) .
Final Answer Therefore, the factored form of g 2 − 36 is ( g − 6 ) ( g + 6 ) .
Examples
Factoring the difference of squares is a useful technique in many areas of mathematics and physics. For example, in physics, you might encounter an expression like v 2 − u 2 , where v is the final velocity and u is the initial velocity of an object. Factoring this as ( v − u ) ( v + u ) can simplify calculations when you're trying to find the change in momentum or kinetic energy. Similarly, in engineering, you might use this technique to simplify expressions related to stress and strain in materials.
The expression g 2 − 36 can be factored as ( g − 6 ) ( g + 6 ) . This is recognized as a difference of squares, g 2 being a square and 36 being 6 2 . By applying the difference of squares formula, we arrive at the final factored form.
;
