Question

the answer
Factorise:
4x2 + 20xy + 25y2 , when x=(-1), y=3
​

Answer 1

Answer:

98

Step-by-step explanation:

4x2 + 20(-1)(3) + 25(3)(2)

8 - 60 +  150

98

Answer 2

Answer:

4

x

2

+

20

x

y

+

25

y

2

=

(

2

x

+

5

y

)

2

Step-by-step explanation:

4

x

2

−

20

x

y

+

25

y

2

4x2-20xy+25y2

Rewrite

4

x

2

4x2

as

(

2

x

)

2

(2x)2

.

(

2

x

)

2

−

20

x

y

+

25

y

2

(2x)2-20xy+25y2

Rewrite

25

y

2

25y2

as

(

5

y

)

2

(5y)2

.

(

2

x

)

2

−

20

x

y

+

(

5

y

)

2

(2x)2-20xy+(5y)2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

20

x

y

=

2

⋅

(

2

x

)

⋅

(

5

y

)

20xy=2⋅(2x)⋅(5y)

Rewrite the polynomial.

(

2

x

)

2

−

2

⋅

(

2

x

)

⋅

(

5

y

)

+

(

5

y

)

2

(2x)2-2⋅(2x)⋅(5y)+(5y)2

Factor using the perfect square trinomial rule

a

2

−

2

a

b

+

b

2

=

(

a

−

b

)

2

a2-2ab+b2=(a-b)2

, where

a

=

2

x

a=2x

and

b

=

5

y

b=5y

.

(

2

x

−

5

y

)

2

(2x-5y)2