Factorise: 50y^2 – 98
Answers
STEP
1
:
Equation at the end of step 1
(2•52y2) - 98 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
50y2 - 98 = 2 • (25y2 - 49)
Trying to factor as a Difference of Squares:
3.2 Factoring: 25y2 - 49
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 : 25 is the square of 5
Check : 49 is the square of 7
Check : y2 is the square of y1
Factorization is : (5y + 7) • (5y - 7)
Equation at the end of step
3
:
2 • (5y + 7) • (5y - 7) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Equations which are never true:
4.2 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Answer:
2(25y²-49)
2(5y²-7²)
2(5y-7) (5y+7)