Factorise the expression 10a^2b + 20ab^2
Answers
Answer:
Changes made to your input should not affect the solution:
(1): "b4" was replaced by "b^4".
STEP
1
:
Equation at the end of step 1
((10•(a2))-(20a•(b2)))+(2•5b4)
STEP
2
:
Equation at the end of step
2
:
((10 • (a2)) - (22•5ab2)) + (2•5b4)
STEP
3
:
Equation at the end of step
3
:
((2•5a2) - (22•5ab2)) + (2•5b4)
STEP
4
:
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
10a2 - 20ab2 + 10b4 = 10 • (a2 - 2ab2 + b4)
Trying to factor a multi variable polynomial :
5.2 Factoring a2 - 2ab2 + b4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (a - b2)•(a - b2)
Detecting a perfect square :
5.3 a2 -2ab2 +b4 is a perfect square
It factors into (a-b2)•(a-b2)
which is another way of writing (a-b2)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Trying to factor as a Difference of Squares:
5.4 Factoring: a-b2
Put the exponent aside, try to factor a-b2
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 : a1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Final result :
10 • (a - b2)