Respuestas
Respuesta:
Explicación paso a paso:
(a + 1) • (a - 1) • (a + 3) • (a - 3)
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a2" was replaced by "a^2". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((a4) - (2•5a2)) + 9
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring a4-10a2+9
The first term is, a4 its coefficient is 1 .
The middle term is, -10a2 its coefficient is -10 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9
Step-2 : Find two factors of 9 whose sum equals the coefficient of the middle term, which is -10 .
-9 + -1 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and -1
a4 - 9a2 - 1a2 - 9
Step-4 : Add up the first 2 terms, pulling out like factors :
a2 • (a2-9)
Add up the last 2 terms, pulling out common factors :
1 • (a2-9)
Step-5 : Add up the four terms of step 4 :
(a2-1) • (a2-9)
Which is the desired factorization
Trying to factor as a Difference of Squares :
2.2 Factoring: a2-1
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 1 is the square of 1
Check : a2 is the square of a1
Factorization is : (a + 1) • (a - 1)
Trying to factor as a Difference of Squares :
2.3 Factoring: a2 - 9
Check : 9 is the square of 3
Check : a2 is the square of a1
Factorization is : (a + 3) • (a - 3)
Final result :
(a + 1) • (a - 1) • (a + 3) • (a - 3)