i. x2 + 5xy + 9xy2 + 45y3 ii. 2y^2x − 10y^2 − x^2y + 5xy iii. x^2 + x − 30 iv. 343x^3 − 1 Factorize these

i. The given expression is x^2 + 5xy + 9xy^2 + 45y^3. This can be factored by grouping:

x^2 + 5xy + 9xy^2 + 45y^3 = x(x + 5y) + 9y^2(x + 5y) = (x + 9y^2)(x + 5y)

ii. The given expression is 2y^2x − 10y^2 − x^2y + 5xy. This can be factored by grouping:

2y^2x − 10y^2 − x^2y + 5xy = 2y^2(x - 5) - xy(x - 5) = (2y^2 - xy)(x - 5)

iii. The given expression is x^2 + x − 30. This is a quadratic expression and can be factored using the formula for factoring quadratics:

x^2 + x − 30 = (x - 5)(x + 6)

iv. The given expression is 343x^3 − 1. This is a difference of cubes and can be factored using the formula for factoring difference of cubes:

343x^3 − 1 = (7x - 1)(49x^2 + 7x + 1)