What is the simplified form of ($$2a^2$$ - 3ab + $$4b^2)$$(a - b)?
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$$2a^3$$ - $$4a^2b$$ + $$b^3$$
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$$2a^3$$ - $$5ab^2$$ - $$4b^2$$
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$$2a^3$$ - $$5a^2b$$ + $$7ab^2$$ - $$4b^3$$
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$$2a^3$$ - $$3a^2b$$ + $$7ab^2$$ - $$4b^3$$
We start with the expression ($$2a^2$$ - 3ab + $$4b^2)$$(a - b). This is a product of two expressions: $$2a^2$$ - 3ab + $$4b^2$$ and a - b.
To simplify this, we distribute each term in the first expression by each term in the second expression. This is like using the distributive property of multiplication over addition (or subtraction).
First, we multiply each term in the first expression by a from the second expression. This gives us $$2a^3$$ - $$3a^2b$$ + $$4ab^2$$.
Then, we multiply each term in the first expression by -b from the second expression. This gives us -$$2a^2b$$ + $$3ab^2$$ - $$4b^3$$.
We then subtract this second set of terms from the first set of terms to get $$2a^3$$ - $$3a^2b$$ + $$4ab^2$$ - (-$$2a^2b$$ + $$3ab^2$$ - $$4b^3)$$, which simplifies to $$2a^3$$ - $$5a^2b$$ + $$7ab^2$$ - $$4b^3$$.
So, the simplified form of the original expression is $$2a^3$$ - $$5a^2b$$ + $$7ab^2$$ - $$4b^3$$.
