Factorise the following using suitable identities...
16x4 – 54x
Answers
Step-by-step explanation:
Pull out like factors :
16x4 - 54x = 2x • (8x3 - 27)
Trying to factor as a Difference of Cubes:
3.2 Factoring: 8x3 - 27
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 8 is the cube of 2
Check : 27 is the cube of 3
Check : x3 is the cube of x1
Factorization is :
(2x - 3) • (4x2 + 6x + 9)
Trying to factor by splitting the middle term
3.3 Factoring 4x2 + 6x + 9
The first term is, 4x2 its coefficient is 4 .
The middle term is, +6x its coefficient is 6 .
The last term, "the constant", is +9
Step-1 : Multiply the coefficient of the first term by the constant 4 • 9 = 36
Step-2 : Find two factors of 36 whose sum equals the coefficient of the middle term, which is 6 .
-36 + -1 = -37 -18 + -2 = -20 -12 + -3 = -15 -9 + -4 = -13 -6 + -6 = -12 -4 + -9 = -13
Observation : No two such factors can be found !!
Hope it helps you