7) Multiply and simplify each expression completely. a) (3n+2)(2n+5) b) (4a-1)^2 c) (2x-5)(x^2+3x+2)

1. Expand the expression $(3n+2)(2n+5)$<br /> Use the distributive property: $a(b+c) = ab + ac$.<br /> $(3n+2)(2n+5) = 3n \cdot 2n + 3n \cdot 5 + 2 \cdot 2n + 2 \cdot 5 = 6n^2 + 15n + 4n + 10$.<br /><br />2. Simplify the expression $6n^2 + 15n + 4n + 10$<br /> Combine like terms: $6n^2 + (15n + 4n) + 10 = 6n^2 + 19n + 10$.<br /><br />3. Expand the expression $(4a-1)^2$<br /> Use the formula for a square: $(a-b)^2 = a^2 - 2ab + b^2$.<br /> $(4a-1)^2 = (4a)^2 - 2(4a)(1) + 1^2 = 16a^2 - 8a + 1$.<br /><br />4. Expand the expression $(2x-5)(x^2+3x+2)$<br /> Distribute each term in the first polynomial across the second polynomial.<br /> $2x(x^2+3x+2) = 2x^3 + 6x^2 + 4x$ and $-5(x^2+3x+2) = -5x^2 - 15x - 10$.<br /><br />5. Simplify the expression $2x^3 + 6x^2 + 4x - 5x^2 - 15x - 10$<br /> Combine like terms: $2x^3 + (6x^2 - 5x^2) + (4x - 15x) - 10 = 2x^3 + x^2 - 11x - 10$.