Can anyone help me with these questions? Please
1. ac - bc + ad - bd
2. xy - 3x - 8y + 24
3. 4x2 + 20x + 5y +xy
4. 48x2y + 20xz +12xy + 5z
is the 4x2 4 times 2 or 4x to the power of two or 4 times x times 2?
same question with 48x2y.
its to the 2nd power
Of course, I can help you with these questions!
1. To simplify the expression ac - bc + ad - bd, you can combine like terms. In this case, the like terms are the ones with the same variables raised to the same power. So, you can combine ac and ad to get a(c + d), and bc and bd to get b(c + d). This gives you the simplified expression (a - b)(c + d).
2. In the expression xy - 3x - 8y + 24, you can also combine like terms. Here, xy, -3x, -8y, and 24 are all separate terms. To simplify it further, you can factor out common factors. Factoring out an x gives you: x(y - 3) - 8y + 24. This can be further simplified as: x(y - 3) - 8(y - 3). Now, you can see that (y - 3) is a common factor in both terms, so you can write it as (x - 8)(y - 3).
3. The expression 4x^2 + 20x + 5y + xy contains both constants and variables. To simplify it, you can group the like terms. So, the terms 4x^2 and xy have the same variables raised to the same power (x^2). Combining them, you get x(x + 4). The other two terms, 20x and 5y, don't have any common variables, so you keep them as they are. Therefore, the simplified form of the expression is x(x + 4) + 20x + 5y.
4. The expression 48x^2y + 20xz + 12xy + 5z also contains constants and variables. Similar to the previous examples, you can group the like terms together. Here, the terms 48x^2y and 12xy both involve the variable 'x' raised to the power of 1 and the variable 'y'. Combining these, you get (48x^2 + 12x)y. The terms 20xz and 5z contain common factors of 'z', so you can factor it out: z(20x + 5). Simplified expression would then be (48x^2 + 12x)y + z(20x + 5).
Regarding your question about the notation, "4x^2" means 4 times x raised to the power of 2. Similarly, "48x^2y" means 48 times x raised to the power of 2 times y. It does not mean 4 times 2 or 4 times x times 2.