x2-y2+4y-4 factorize correctly plz
Answers
Answer:
The rule to factorise any quadratic is to find two numbers such that
product
=
x
2
coefficient
×
constant coefficient
sum
=
x
coefficient
So for
y
2
−
4
y
−
4
we seek two numbers such that
product
=
(
1
)
⋅
4
)
=
4
sum
=
−
4
So we look at the factors of
4
. As the sum is negative and the product is positive then both of the factors must be negative, We can check every combination of the product factors:
factor1
factor2
sum
4
1
5
2
2
4
−
4
−
1
−
5
−
2
−
2
−
4
So the factors we seek are
−
2
and
−
2
Therefore we can factorise the quadratic as follows:
y
2
−
4
y
−
4
=
y
2
−
2
y
+
−
2
y
+
4
∴
y
2
−
4
y
+
4
=
y
(
y
−
2
)
−
2
y
(
y
−
2
)
∴
y
2
−
4
y
+
4
=
(
y
−
2
)
(
y
−
2
)
∴
y
2
−
4
y
+
4
=
(
y
−
2
)
2
This approach works for all quadratics (assuming it does factorise) , The middle step in the last section can usually be skipped with practice.
An important quadratic relationship to be familiar with is;
(
a
+
b
)
2
=
a
2
+
2
a
b
+
b
2
With this we can spot intermediately that
y
2
−
4
y
+
4
is a perfect square...
Step-by-step explanation:
Here
x² - y² + 4y -4
(x)² -(y²) +4y - 4
( x + y) ( x - y) + 4( y - 1)