Question

Factorise fully 50 - 2y2​

Answer 1

50 - 2y2
STEP
2
:

STEP
3
:
Pulling out like terms

3.1 Pull out like factors :

50 - 2y2 = -2 • (y2 - 25)

Trying to factor as a Difference of Squares:

3.2 Factoring: y2 - 25

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 : y2 is the square of y1

Factorization is : (y + 5) • (y - 5)

Final result :
-2 • (y + 5) • (y - 5)