Answer:
To find the product of the given expressions:
(i) \((x + y - 3)(4x - 7y + 2)\)
We'll use the distributive property to expand the expression:
\[
= x(4x - 7y + 2) + y(4x - 7y + 2) - 3(4x - 7y + 2)
\]
\[
= 4x^2 - 7xy + 2x + 4xy - 7y^2 + 2y - 12x + 21y - 6
\]
\[
= 4x^2 - 7xy + 4xy - 7y^2 + 2x + 2y - 12x + 21y - 6
\]
\[
= 4x^2 - 7y^2 - 10x + 23y - 6
\]
So, the product is \(4x^2 - 7y^2 - 10x + 23y - 6\).
(iii) \((x^2 - 7x + 2)(x^2 + 5x - 4)\)
Again, using the distributive property:
\[
= x^2(x^2 + 5x - 4) - 7x(x^2 + 5x - 4) + 2(x^2 + 5x - 4)
\]
\[
= x^4 + 5x^3 - 4x^2 - 7x^3 - 35x^2 + 28x + 2x^2 + 10x - 8
\]
\[
= x^4 - 2x^3 - 37x^2 + 38x - 8
\]
So, the product is \(x^4 - 2x^3 - 37x^2 + 38x - 8\).
