Mathematics
Simplify:
(i) 5x + 3y - 8z + 2y - 3x + 5z + z - 7y - 2x
(ii) 4x3 - 2x2 + 5x - 1 + 8x + x2 - 6x3 + 7 - 6x + 3 - 3x2 - x3
(iii) 2x2 + 3xy - 3y2 + x2 - xy + y2
(iv) 2 - 3z2 + 5yz + 7y2 - 8 + z2 - 6yz - 9y2 + 1 - 2z2 - 2yz - y2
(v) 2m - 3n + 5p + 2m + n - 2p - 3m - 4n + p
Answer
(i) 5x + 3y - 8z + 2y - 3x + 5z + z - 7y - 2x
Arranging the like terms together, we have:
5x + 3y - 8z + 2y - 3x + 5z + z - 7y - 2x
= (5x - 3x - 2x) + (3y + 2y - 7y) + (-8z + 5z + z)
Combining coefficients:
= (5 - 3 - 2)x + (3 + 2 - 7)y + (-8 + 5 + 1)z
= (0)x + (-2)y + (-2)z
= -2y - 2z
Hence, the answer is -2y - 2z
(ii) 4x3 - 2x2 + 5x - 1 + 8x + x2 - 6x3 + 7 - 6x + 3 - 3x2 - x3
Arranging the like terms together, we have:
4x3 - 2x2 + 5x - 1 + 8x + x2 - 6x3 + 7 - 6x + 3 - 3x2 - x3
= (4x3 - 6x3 - x3) + (-2x2 + x2 - 3x2) + (5x + 8x - 6x) + (-1 + 7 + 3)
Combining coefficients:
= (4 - 6 - 1)x3 + (-2 + 1 - 3)x2 + (5 + 8 - 6)x + (9)
= (-3)x3 + (-4)x2 + (7)x + 9
= -3x3 - 4x2 + 7x + 9
Hence, the answer is -3x3 - 4x2 + 7x + 9
(iii) 2x2 + 3xy - 3y2 + x2 - xy + y2
Arranging the like terms together, we have:
2x2 + 3xy - 3y2 + x2 - xy + y2
= (2x2 + x2) + (3xy - xy) + (-3y2 + y2)
Combining coefficients:
= (2 + 1)x2 + (3 - 1)xy + (-3 + 1)y2
= 3x2 + 2xy - 2y2
Hence, the answer is 3x2 + 2xy - 2y2
(iv) 2 - 3z2 + 5yz + 7y2 - 8 + z2 - 6yz - 9y2 + 1 - 2z2 - 2yz - y2
Arranging the like terms together, we have:
2 - 3z2 + 5yz + 7y2 - 8 + z2 - 6yz - 9y2 + 1 - 2z2 - 2yz - y2
= (2 - 8 + 1) + (-3z2 + z2 - 2z2) + (5yz - 6yz - 2yz) + (7y2 - 9y2 - y2)
Combining coefficients:
= (-5) + (-3 + 1 - 2)z2 + (5 - 6 - 2)yz + (7 - 9 - 1)y2
= -5 + (-4)z2 + (-3)yz + (-3)y2
= -5 - 4z2 - 3yz - 3y2
Hence, the answer is -5 - 4z2 - 3yz - 3y2
(v) 2m - 3n + 5p + 2m + n - 2p - 3m - 4n + p
Arranging the like terms together, we have:
2m - 3n + 5p + 2m + n - 2p - 3m - 4n + p
= (2m + 2m - 3m) + (-3n + n - 4n) + (5p - 2p + p)
Combining coefficients:
= (2 + 2 - 3)m + (-3 + 1 - 4)n + (5 - 2 + 1)p
= (1)m + (-6)n + (4)p
= m - 6n + 4p
Hence, the answer is m - 6n + 4p
Related Questions
Add the following expressions:
(i) 2x2, -5x2, -x2, 6x2
(ii) x2 - 2xy + 3y2, 5y2 + 3xy - 6x2
(iii) 2x + 9y - 7z, 3y + z - 3x, 2z - 4y - x
(iv) 2ab + 3bc - 5ca, 4bc - 3ab + 7ca, 2ca - ab - 5bc
(v) 3x3 + 2x2 - 6x + 3, 2x3 - 3x2 - x - 4, 1 + 2x - 3x2 - 4x3
(vi) 3n2 + 5mn - 6m2, 2m2 - 3mn - 4n2, 2mn - 3m2 - 7n2
(vii) 3z3 - z2 + 5, 1 - 2z + z2, 3 + 2z - z3
The two adjacent sides of a rectangle are 3a - b and 6b - a. Find its perimeter.
Find the perimeter of a triangle whose sides are 2y + 3z, z - y, 4y - 2z.