factor:
(x^2+5x)^2 - 36
and
(a-b)^2 - (c-d)^2
show the steps pleasee!
You got the second one, just reversed
x y = y x !
[ (x^2+5x) - 6 ] [(x^2+5x) + 6 ]
(x^2 + 5 x - 6) (x^2 + 5x + 6)
now if the back of your book says
(x^2 + 5 x + 6)( x^2 + 5 x - 6)
That is the SAME
okay thankyou so much!! :-)
To factor the expressions you provided, we will use a special factoring formula called the difference of squares. The formula states that for any two numbers, let's call them 𝑎 and 𝑏, the expression 𝑎^2 - 𝑏^2 can be factored as (𝑎 + 𝑏)(𝑎 - 𝑏).
Let's solve the two expressions step by step:
1. (𝑥^2 + 5𝑥)^2 - 36:
First, observe that we have a squared term, (𝑥^2 + 5𝑥), and another number being squared, 36. Since the latter is a perfect square (6^2), we can rewrite the expression as follows:
(𝑥^2 + 5𝑥)^2 - 6^2
Now, we can apply the difference of squares formula: (𝑎 + 𝑏)(𝑎 - 𝑏). In this case, 𝑎 = 𝑥^2 + 5𝑥 and 𝑏 = 6. So the expression becomes:
[(𝑥^2 + 5𝑥) + 6][(𝑥^2 + 5𝑥) - 6]
Thus the factored form of (𝑥^2 + 5𝑥)^2 - 36 is [(𝑥^2 + 5𝑥) + 6][(𝑥^2 + 5𝑥) - 6].
2. (𝑎 - 𝑏)^2 - (𝑐 - 𝑑)^2:
Similarly, we apply the difference of squares formula. In this case, 𝑎 = 𝑎, 𝑏 = 𝑏, 𝑐 = 𝑐, and 𝑑 = 𝑑. So the expression can be factored as:
[(𝑎 - 𝑏) + (𝑐 - 𝑑)][(𝑎 - 𝑏) - (𝑐 - 𝑑)]
Therefore, the factored form of (𝑎 - 𝑏)^2 - (𝑐 - 𝑑)^2 is [(𝑎 - 𝑏) + (𝑐 - 𝑑)][(𝑎 - 𝑏) - (𝑐 - 𝑑)].
These are the steps to factor the given expressions using the difference of squares formula.