1) (5х²+8х-7)-(2х²-2х-12) 2) (2х-3)+(-2х²-5х-18) 3) (6а²-3а+11)-(-3а-а²+7) 4) (14ху-9х²-3у²)-(-3х²+5ху-4у²) 5)(7аb²-15ab+3a²b)+(30ab-8a²-b)
Let's simplify each expression step by step.
- \((5x^2 + 8x - 7) - (2x^2 - 2x - 12)\)
First, distribute the negative sign:
\[ = 5x^2 + 8x - 7 - 2x^2 + 2x + 12 \]
Now, combine like terms:
\[ = (5x^2 - 2x^2) + (8x + 2x) + (-7 + 12) \] \[ = 3x^2 + 10x + 5 \]
- \((2x - 3) + (-2x^2 - 5x - 18)\)
Combine like terms:
\[ = 2x - 3 - 2x^2 - 5x - 18 \]
Now, rearranging and combining:
\[ = -2x^2 + (2x - 5x) + (-3 - 18) \] \[ = -2x^2 - 3x - 21 \]
- \((6a^2 - 3a + 11) - (-3a - a^2 + 7)\)
Distributing the negative sign:
\[ = 6a^2 - 3a + 11 + 3a + a^2 - 7 \]
Combining like terms:
\[ = (6a^2 + a^2) + (-3a + 3a) + (11 - 7) \] \[ = 7a^2 + 0a + 4 \] \[ = 7a^2 + 4 \]
- \((14xy - 9x^2 - 3y^2) - (-3x^2 + 5xy - 4y^2)\)
Distributing the negative sign:
\[ = 14xy - 9x^2 - 3y^2 + 3x^2 - 5xy + 4y^2 \]
Combining like terms:
\[ = (-9x^2 + 3x^2) + (14xy - 5xy) + (-3y^2 + 4y^2) \] \[ = -6x^2 + 9xy + y^2 \]
- \((7ab^2 - 15ab + 3a^2b) + (30ab - 8a^2 - b)\)
Combining like terms:
\[ = 7ab^2 + (-15ab + 30ab) + (3a^2b - 8a^2) - b \] \[ = 7ab^2 + 15ab + (3a^2b - 8a^2) - b \]
Further simplifying gives:
\[ = 7ab^2 + 15ab + 3a^2b - 8a^2 - b \]
If combined further:
\[ = 7ab^2 + (15ab - b) + 3a^2b - 8a^2 \] \[ = 7ab^2 + 14ab + 3a^2b - 8a^2 \]
Your final answers are:
- \(3x^2 + 10x + 5\)
- \(-2x^2 - 3x - 21\)
- \(7a^2 + 4\)
- \(-6x^2 + 9xy + y^2\)
- \(7ab^2 + 14ab + 3a^2b - 8a^2\)
