Question

(3a^2-ab)(9a^4+3a^3b+a^2b^2)

Answer 1

Відповідь: вроді так

Answer 2

To multiply the two expressions, you can use the distributive property (also known as FOIL for binomials). Here's the step-by-step process:

Expression 1: $3a^2 - ab$ Expression 2: $9a^4 + 3a^3b + a^2b^2$

1. Multiply the first term of Expression 1 by every term in Expression 2: $3a^2 \cdot 9a^4 + 3a^2 \cdot 3a^3b + 3a^2 \cdot a^2b^2$

2. Multiply the second term of Expression 1 by every term in Expression 2: $-ab \cdot 9a^4 - ab \cdot 3a^3b - ab \cdot a^2b^2$

Now, let's simplify each of these multiplications:

1. $3a^2 \cdot 9a^4 = 27a^6$ $3a^2 \cdot 3a^3b = 9a^5b$ $3a^2 \cdot a^2b^2 = 3a^4b^2$

2. $-ab \cdot 9a^4 = -9a^5b$ $-ab \cdot 3a^3b = -3a^4b^2$ $-ab \cdot a^2b^2 = -a^3b^3$

Now, add all the terms together:

$27a^6 + 9a^5b + 3a^4b^2 - 9a^5b - 3a^4b^2 - a^3b^3$

Next, combine like terms:

$27a^6 + (9a^5b - 9a^5b) + (3a^4b^2 - 3a^4b^2) - a^3b^3$

The terms $9a^5b$ and $-9a^5b$ cancel each other out, as do the terms $3a^4b^2$ and $-3a^4b^2$. This leaves us with:

$27a^6 - a^3b^3$

So, the product of the two expressions $3a^2 - ab$ and $9a^4 + 3a^3b + a^2b^2$ is $27a^6 - a^3b^3$.