4x2 9. 8x37x-12; -5x2 + 11; -6x3 + x2 - 3x; 10. 3x2 + 2xy + 5xy2 + y3; 3xy 3xy2+2x2 11. 3a2 - ab + ac 12. x - x3 + xy. 5bc; -2a2 6bc + b2 + 3c2. 3x3 + 6x25x + 3; 2x3- x1 + 5x2-6x-5; -3x4x2 - x; 5x2-x+6x+2. ; 13. 6xу2 — 8y3 - 2x2y - x3; 12xy2 + 4x3 — 10xz2 + y3; 6xy2 -xz2 + x2y + 3xy2 - 2y2; 8x3- 6xz2 - 2y2 + 3z2 — xy2. 14. 2a43a3 + 4a25a + 6; 4a3 3a4 + 6a - 8; 6a73a3; 5a3 a4 + a2 + 7a + 9. 6v3 - 15. u3 + 2uv2 - u2v - v3; 2u3 + 3u2v + 4uv2 + 6v3; 5uv2 u3. 17. m5 + 3m3n2 - 4mn1; 4m1n - 2m2n3 + n3; -2m3 + 6m3n - 2n5; 5m1n - 2m3n2 + 6m2n3 — 2mn1. 18. x2y 2xy2-4y3 1; 2 + xy2+ y3; 6 - 4x2y + xy2; -x2y - 7+ 3xy2; 5y3 + 23x2y xy2. 19. a3 - b3; a2 + ab + b2; 2a3 3a2b+3ab2 b3; 4a2b6ab2; -a3+3a2b3ab2b3; 4ab2+6a2b+ a3 + b3. 20. 2x2 + 3y2+4z2 - 6xy; x2 + 5xz 3yz; y2-22 + 2xyz; 6xy+4yz - 3xyz + 22; -2yz - x2 - y2 + ¿2. SUBTRACTION OF INTEGRAL COMPOUND EXPRESSIONS 33. To subtract one compound expression from another, we indicate the subtraction by placing a minus sign between the minuend and subtrahend. Thus, the subtraction of a + b c from a+b+c is written, a + b + c − (a + b — c). Combining like terms, the remainder becomes 2c. Hence the Rule for subtracting one compound expression from another: Change the signs of the subtrahend and add. For convenience, we follow the method used in addition, writing like terms under each other. 10. From 2x4. 3x3 +- 4x2 5x 10 take 2x3 - 3b2. 7ab 6a2 Find the expression for A - B - C + D. This problem means that the expressions represented by A, B, C, and D are to be combined by addition or subtraction, according to the signs that connect them. This can most conveniently be done in a single addition by remembering that the subtrahend must have its signs changed before being added to the minuend. Using the same values for A, B, C, D, find the expression REMOVAL OF PARENTHESES 34. Expressions may occur, having one sign of aggregation inside of another. For this purpose we use the different signs, parenthesis (), bracket [], brace {}, and vinculum The rules for removing a parenthesis are applied here and it is usual to remove one sign of aggregation at a time, beginning with the innermost. (845t +7). (27a-4b11ab) - (-6b - 13by + 17ab). (3y4x)+(4x - 2y)}. {8x { 8. {a [a (b − c) — (a + b + c]}. 9. {[(-a-b-cd)]}. 10. − { + [ − (− a + b + c− d) + a] — b}. 11. 5a + {-3a + [3a − (2a + a − b)] + a}. {5y [x (2z + 3y) + x − (y+2x-2)]}. INSERTION OF PARENTHESES 35. The insertion of various terms in a parenthesis is the reverse of the removal of a parenthesis and hence the same rules are observed. Since a + (b + c) = a + b + c ..a + b + c = a + (b + c) 1. Any number of terms may be enclosed in a parenthesis, preceded by a plus sign, without changing the signs of these terms. 2. Any number of terms may be enclosed in a parenthesis, preceded by a minus sign, by changing the signs of these In the following expressions, enclose the last three terms in a parenthesis, preceded by a minus sign. 1. 10t2t1-13 - t. 2. 4x8 5t - 4. 3. 177a4b11ab 13 by. In algebraic addition, like terms are added by adding their coefficients, using the sum of these coefficients as the coefficient of the sum. Thus, 3x 2x + 5x = 6x. If the coefficients are literal, and therefore cannot be actually combined by addition, this addition is indicated by enclosing these coefficients in a parenthesis. Thus, ax + bx x = (a + b − 1)x. In the following expressions, collect like terms by enclosing their coefficients in parentheses: 11. ax + by + cz + bx - az + y = Note that these coefficients are preferably arranged in alphabetical order and if the first of any set of coefficients is negative, a minus sign is used before the parenthesis. 12. ax+2ay + 42 + bx 13. 2ax 2by 2cz 14. 3by 15. 5az Зах 3y 4by+3cz+2bx 7cx 5cy + xy + z. az ay acx + bcz 6by + 4az 4bx 2ay + 4cz 19. ах 10az + 4by 2cx+by+bz. xy, and R = x2 + xy + y2, find the value of 5. Simplify: — [x2 − (1 − x)] − {1 + [x2 x3 + x3]}. 6. Simplify: a + 2b + (14a 4a-4b)}. 2)] — [x + (5y 7. Simplify: a2+ 5 −[2ab - {− (7 — 3ab) — ab + 2a2 — z} |