Find the difference of x^{2} + xy + y^{2} + yz and 2x^{2} – 3xy – y^{2} – yz.
2x^{2} – 3xy – y^{2}– yz – (x^{2}– xy + y^{2} + yz)
= 2x^{2} – 3xy – y^{2}– yz – x^{2} + xy – y^{2}– yz
= x^{2} – 2xy – 2y^{2}– 2yz
What is the result when the sum of (–5x^{2} + 7xy + 2y^{2}) and (x^{2} – 3xy – y^{2}) is subtracted from –7?
Sum = –5x^{2} + 7xy + 2y^{2} + x^{2} – 3xy – y^{2}
= – 4x^{2} + 4xy + y^{2}
= –7 –(– 4x^{2} + 4xy + y^{2})
= –7 + 4x^{2}– 4xy – y^{2})
What is the product of (0.8m – 0.7n) and (1.5n – 1.7m)?
(0.8m – 0.7n) (1.5n – 1.7m)
= (0.8m)(1.5n) + (0.7n) (1.7m) – (0.7n)(1.5n) – (0.8m) (1.7m)
= 1.2mn + 1.19mn –1.05n^{2} –1.36m^{2}
= 2.39mn – 1.05n^{2} – 1.36m^{2}
Find the sum of 0.3x^{2}– 3xy + 0.8y^{2} and 4x^{2} – 2y^{2} + 0.7xy?
0.3x^{2} – 3xy + 0.8y^{2} + 4x^{2} – 2y^{2} + 0.7xy
= (4 + 0.3) x^{2} + (0.7 – 3) xy + (0.8 – 2)y^{2}
= 4.3x^{2} – 2.3xy –1.2y^{2}
Find the product of (7x^{2} – x + 11) and (x^{2} – 3).
(7x^{4}– x + 11) (x^{2}– 3)
= 7x^{4} – 21x^{2}– x^{3} + 3x + 11x^{2} – 33
= 7x^{4}– x^{3} – 10x^{2} + 3x – 33
What is the product of 1.5 a(10a^{2}b – 100ab^{2})
1.5a(10a^{2}b –100ab^{2})
= 15a^{3}b – 150a^{2}b^{2}
Find the simplified expression of 7x^{2} – [x^{2}– 3x –{x + y}] – (5x – 3y + 3).
7x^{2} – [x^{2}– 3x –{x + y}] – (5x – 3y + 3)
= 7x^{2} – x^{2} – 3x – x + y – 5x + 3y – 3
= 6x^{2 }– x + 4y – 3
Find the result of x(x + 4) + 3x (2x^{2 }– 3) + 4x^{2} + 5?
x(x + 4) + 3x (2x^{2}– 3) +4x^{2} + 5
= x 2 + 4x + 6x^{3}– 9x + 4x^{2} + 5
= 6x^{3} + 5x^{2}– 5x + 5
4mn (m – n) – 6m^{2}(n – n^{2}) – 3n^{2}(2m^{2} – m) = ?
4mn(m – n) – 6m^{2}(n – n^{2}) –3n^{2}(2m^{2} – m)
= 4 m^{2}n – 4m – n^{2} – 6m^{2}n + 6m^{2} n^{2} – 6n^{2}m^{2} + 3n^{2}m
= –2m^{2}n – n^{2}m = –mn(2m + n)
a^{2}b(a – b^{2}) – ab^{2} (3ab – a^{2}) – a^{3}b (1– 2b) = ?
a^{2}b(a – b^{2}) –ab^{2}(3ab – a^{2}) – a^{3}b (1 – 2b)
= a^{3}b – a^{2}b^{3} – 3a^{2}b^{3} + a^{3}b^{2} – a^{3}b + 2a^{3}b^{2}
= 3a^{3}b^{2}– 4a^{2}b^{3}
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