Question

(a²-7ab+2b²) (2a+3b)​

Answer 1

$(a^2-7ab+2b^2)(2a+3b) = a^2(2a+3b)-7ab(2a+3b)+2b^2(2a+3b)= \\= 2a^3+3a^2b-14a^2b-21ab^2+4ab^2+6b^3 = 2a^3-11a^2b-17ab^2+6b^3$

Answer 2

To simplify the given expression $(a^2 - 7ab + 2b^2) \cdot (2a + 3b)$, you can use the distributive property (also known as the FOIL method) to multiply the terms in each binomial. The distributive property states that $a \cdot (b + c) = a \cdot b + a \cdot c$. Applying this property to your expression:

$$\begin{align*} &(a^2 - 7ab + 2b^2) \cdot (2a + 3b) \\ &= a^2 \cdot (2a + 3b) - 7ab \cdot (2a + 3b) + 2b^2 \cdot (2a + 3b) \\ &= 2a^3 + 3a^2b - 14a^2b - 21ab^2 + 4ab^2 + 6b^3 \\ &= 2a^3 - 11a^2b - 17ab^2 + 6b^3 \end{align*}$$

So, the simplified expression is $2a^3 - 11a^2b - 17ab^2 + 6b^3$.