Answer:
Explanation:
Addition:
a) 9pq - 5pq + 3pq - pq = 6pq
b) 3p - 4q + 2p - 3q = 5p - 7q
c) 4x² + 3y² + 4xy + 5x² + 8y² + 12xy = 9x² + 11y² + 16xy
d) 3pq + 4qr + 8r² + 4pq + 6pr + 4p² + 8pr + 2p²
= 7pq + 4qr + 8r² + 14pr + 6p²
= 7p(q + 2r) + 2(2qr + 4r² + 3p²)
e) .5x + 2y² - .8xy + .8x² + 4y² + .8xy
= .5x + 6y² + .8x²
= x(.5 + .8x) + 6y²
f) 5a - 8b + 2c -4b + 3c - 2a + 6b - c - a
= 2a - 6b + 4c
= 2(a - 3b + 2c)
Subtraction:
term which comes after from will come as the first term for subtraction:
a) a - 2b - 5c - 8 - (-6a + b + 3c + 8)
= a - 2b - 5c - 8 + 6a - b - 3c - 8
= 7a - 3b - 8c - 16
= 7a - 3b - 8(c + 2)
b) 25x² + 16xy - 3a² - 2 - (13xy - 6x² + 4a² - 1)
= 25x² + 16xy - 3a² - 2 - 13xy + 6x² - 4a² + 1
= 31x² + 3xy - 7a² - 1
c) 8x - 20xy + 10y + 4 - (4x - 12xy + 8y - 3)
= 8x - 20xy + 10y + 4 - 4x + 12xy - 8y + 3
= 4x - 8xy + 2y + 7
= 4x(1 - 2y) + 2y + 7
d) 4x² - 8x - 5y² - 5 - (2x² - 3x - 4y² + 2)
= 4x² - 8x - 5y² - 5 - 2x² + 3x + 4y² - 2
= 2x² - 5x - y² - 7
e)4x²y + 5xy + 2y²x - 3 - (4x²y + 3xy - 4y²x + 2)
= 4x²y + 5xy + 2y²x - 3 - 4x²y - 3xy + 4y²x - 2
= 2xy + 6y²x - 5
= 2xy(1 + 3y) - 5
f) .9x² + .8x + 5 - (.4x² - .2x - 1)
= .9x² + .8x + 5 - .4x² + .2x + 1
= .5x² + x + 6
Addition than Subtraction:
sum = 3l - 4m - 7n² + 2l + 3m - 4n²
= 5l - m - 11n²
subtraction = 6l + 3m + n² - (5l - m - 11n²)
= 6l + 3m + n² - 5l + m + 11n²
= l + 4m + 12n²
= l + 4(m + 3n²)
Addition than Subtraction:
sum = x - 3y + 2z - 4x + 9y - 11z
= -3x + 6y - 9z
subtraction = -3x + 6y - 9z - (3x - 4y - 7z)
= -3x + 6y - 9z - 3x + 4y + 7z
= -6x + 10y - 2z
= 2(-3x + 5y - z)
Products:
a) 3xy * 5x * 0 = 0
b) -2x² * 7a²x * 6a³x * 7 * 5 = -2940x⁴a⁵
c) 3 * 15x * -23x²y = -1035x³y
d) 6 * 5 * ab * 12 * 6 * bc * 5 * 6 * abc
= 64800a²b³c²
e) 12xy(3x - 6y) = 36x²y - 72xy²
f) xz(x + y) = x²z + xyz
g) -4y(2z - 3x) = -8yz + 12xy
h) 1.5x(10x²y - 100xy²) = 15x³y - 150x²y²
i) (5x + 3)(7x + 2)
= 35x² + 10x + 21x + 6
= 35x² + 31x + 6
j) (3x² + y²)(2x² + 3y²)
= 6x⁴ + 9x²y² + 2x²y² + 3y⁴
= 6x⁴ + 11x²y² + 3y⁴
k) (3x - 5y)(x + y)
= 3x² + 3xy - 5xy - 5y²
= 3x² - 2xy - 5y²