Question

4(2a-3)^2-3(2a-3)(a-1)-7(a-1)^2​

Answer 1

Let (2a - 3) be x and (a - 1) be y.

4(2a - 3)^2 - 3(2a - 3)(a - 1) - 7(a - 1)^2

= 4x^2 - 3xy - 7y^2

= 4x^2 - 7xy + 4xy - 7y^2

= (4x^2 - 7xy) + (4xy - 7y^2)

= x(4x - 7y) + y(4x - 7y)

= (x + y)(4x - 7y)

= ((2a - 3) + (a - 1))(4(2a - 3) - 7(a - 1))

= (2a - 3 + a - 1)(8a - 12 - 7a + 7)

= (3a - 4)(a - 5)

Answer 2

Answer:

a = 5 or 4/3

Step-by-step explanation:

$= 4(2a - 2 - 1)^{2} - 3(2a - 2 - 1)(a - 1) - 7(a - 1)^{2} \\ = 4(2(a - 1) - 1)^{2} - 3(2(a - 1) - 1)(a - 1) - 7(a - 1)^{2} \\ = 4(4(a - 1)^{2} + 1 - 4(a - 1)) - 3(2(a - 1) - 1)(a - 1) - 7(a - 1)^{2} \\ = 16(a - 1)^{2} + 4 - 16(a - 1) - 6(a - 1)^{2} + 3(a - 1) - 7(a - 1)^{2} \\ = 3(a - 1)^{2} - 13(a - 1) + 4 \\ we \: take \: \: x = a - 1 \\ (x - 4)(3x - 1) \\ ((a - 1) - 4)(3(a - 1) - 1) \\ (a - 5)(3a - 4) \\ a = 5 \: or \\ a = \frac{4}{3}$