simplify using formula (4a2-9)(4a2-6a+9)(4a2+6a+9)
Answers
Answer:
(4a
2
−9)(4a
2
−6a+9)(4a
2
+6a+9)=(2a−3)
3
(2a+3)
3
Step-by-step explanation:
Given : Expression (4a^2-9)(4a^2-6a+9)(4a^2+6a+9)(4a
2
−9)(4a
2
−6a+9)(4a
2
+6a+9)
To find : Solve the expression by formula ?
Solution :
Using algebraic identity,
a^2\pm 2ab+b^2=(a\pm b)^2a
2
±2ab+b
2
=(a±b)
2
a^2-b^2=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
We can write the expression as,
=((2a)^2-(3)^2)((2a)^2-2\cdot 3\cdot 2a+(3)^2)((2a)^2+2\cdot 3\cdot 2a+(3)^2)=((2a)
2
−(3)
2
)((2a)
2
−2⋅3⋅2a+(3)
2
)((2a)
2
+2⋅3⋅2a+(3)
2
)
=(2a+3)(2a-3)(2a-3)^2(2a+3)^2=(2a+3)(2a−3)(2a−3)
2
(2a+3)
2
=(2a-3)^3(2a+3)^3=(2a−3)
3
(2a+3)
3
Therefore, (4a^2-9)(4a^2-6a+9)(4a^2+6a+9)=(2a-3)^3(2a+3)^3(4a
2
−9)(4a
2
−6a+9)(4a
2
+6a+9)=(2a−3)
3
(2a+3)
3
#Learn more
( - 2a2 + 6b +9) - ( 4a2 -2b- 7 )
