Question

4x² – 9(2x - y)² factorise it​

Answer 1

Answer:

hello mate!,

Step-by-step explanation:

we need to factorise, this expression

but before, we need to simplify it

4x²-9(2x-y)²= using Identity 2(a-b)²=a²-2ab+b²

a=2x, b=y,(2x)²=4x², 2(2x)(y)=4xy, y²

4x²-9(4x²-4xy+y²)

16x⁴-16x³y+4x²y²-36x²+36xy-9y²

then we factorise it further,

we could write it as,

16x⁴-16x³y+4x²y²-(36x²-36xy+9y²)

using identity 2, a=6x, b=3y

(6x-3y)²=(6X)²-2(6X)(3Y)+(3y)²

later,

we get it as,

(16x⁴-16x³y+4x²y²)-(6xy-3y)²

using identity 2,

16x⁴-16x³y+4x²y², a=(4x)², b=(2xy)²

hence, (4x²-2xy)²=(4x²)²-2(4x²)(2xy)+(2xy)²

hence,

we got it as

(4x²-2xy)²-(6x-3y)²

is the factorized form

thank you mate!

have a great day ahead!

Answer 2

Step-by-step explanation:

(4 • (x2)) - 9 • (2x - y)2

STEP

2

:

Equation at the end of step

2

:

22x2 - 9 • (2x - y)2

STEP

3

:

3.1 Evaluate : (2x-y)2 = 4x2-4xy+y2

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

-32x2 + 36xy - 9y2 = -1 • (32x2 - 36xy + 9y2)

Trying to factor a multi variable polynomial :

4.2 Factoring 32x2 - 36xy + 9y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (4x - 3y)•(8x - 3y)

Final result :

(3y - 4x) • (8x - 3y)