Answer:
A(x) = 35x² + 54x + 17
Explanation:
Relation in the polynomials has been defined as,
A(x) = L(x).W(x) - M(x).N(x)
L(x) = (6x + 5)
W(x) = (6x + 5)
M(x) = (x + 4)
N(x) = (x + 2)
By substituting the polynomials in the expression,
A(x) = (6x + 5)(6x + 5) - (x + 4)(x + 2)
= (6x + 5)² - (x + 4)(x + 2)
= (36x² + 60x + 25) - (x + 4)(x + 2) [Since, (a + b)² = a² + 2ab + b²]
= (36x² + 60x + 25) - [x(x + 2) + 4(x + 2)]
= (36x² + 60x + 25) - [x² + 2x + 4x + 8]
= (36x² + 60x + 25) - [x² + 6x + 8]
= (36x² - x²) + (60x - 6x) + (25 - 8)
= 35x² + 54x + 17
A(x) = 35x² + 54x + 17