Предмет: Алгебра,
автор: ncharina
Ответы
Автор ответа:
0
![1) \ a^{2} - 64 = a^{2} - 8^{2} = (a - 8)(a + 8) \ 9m^{2} - 25 = (3m)^{2} - 5^{2} = (3m - 5)(3m + 5) \ x^{2} +14xy+ 49 y^{2} = (x + 7y)^{2} = (x + 7y) (x + 7y) \ 2) \ (5x - y)^{2} - (y+5x)^{2}= 25x^{2} - 10xy + y^{2} - y^{2} - 10xy - 25x^{2} = - 20xy \ 3) \ 6,8^{2} = (7-0,2)^{2} = 7^{2} - 2*7*0,2 + 0,2^{2} = 49 - 2,8 + 0,04 = \ = 46,2+ 0,04 = 46,24 \ 31^{3} = (30 + 1)^{3} = 30^{3}+3*30^{2}*1 +3*30*1^{2} + 1^{3} = \ =27000 + 2700 + 90 + 1 = 29 791 \](https://tex.z-dn.net/?f=1%29+%5C+a%5E%7B2%7D+-+64+%3D+a%5E%7B2%7D+-+8%5E%7B2%7D+%3D+%28a+-+8%29%28a+%2B+8%29+%5C+9m%5E%7B2%7D+-+25+%3D+%283m%29%5E%7B2%7D+-+5%5E%7B2%7D+%3D+%283m+-+5%29%283m+%2B+5%29+%5C+x%5E%7B2%7D+%2B14xy%2B+49+y%5E%7B2%7D+%3D+%28x+%2B+7y%29%5E%7B2%7D+%3D+%28x+%2B+7y%29+%28x+%2B+7y%29+%5C+2%29+%5C+%285x+-+y%29%5E%7B2%7D+-+%28y%2B5x%29%5E%7B2%7D%3D+25x%5E%7B2%7D+-+10xy+%2B+y%5E%7B2%7D+-+y%5E%7B2%7D+-+10xy+-+25x%5E%7B2%7D+%3D+-+20xy+%5C+3%29+%5C+6%2C8%5E%7B2%7D+%3D+%287-0%2C2%29%5E%7B2%7D+%3D+7%5E%7B2%7D+-+2%2A7%2A0%2C2+%2B+0%2C2%5E%7B2%7D+%3D+49+-+2%2C8+%2B+0%2C04+%3D+%5C+%3D+46%2C2%2B+0%2C04+%3D+46%2C24+%5C+31%5E%7B3%7D+%3D+%2830+%2B+1%29%5E%7B3%7D+%3D+30%5E%7B3%7D%2B3%2A30%5E%7B2%7D%2A1+%2B3%2A30%2A1%5E%7B2%7D+%2B+1%5E%7B3%7D+%3D+%5C+%3D27000+%2B+2700+%2B+90+%2B+1+%3D+29+791+%5C+ "1) \ a^{2} - 64 = a^{2} - 8^{2} = (a - 8)(a + 8) \ 9m^{2} - 25 = (3m)^{2} - 5^{2} = (3m - 5)(3m + 5) \ x^{2} +14xy+ 49 y^{2} = (x + 7y)^{2} = (x + 7y) (x + 7y) \ 2) \ (5x - y)^{2} - (y+5x)^{2}= 25x^{2} - 10xy + y^{2} - y^{2} - 10xy - 25x^{2} = - 20xy \ 3) \ 6,8^{2} = (7-0,2)^{2} = 7^{2} - 2*7*0,2 + 0,2^{2} = 49 - 2,8 + 0,04 = \ = 46,2+ 0,04 = 46,24 \ 31^{3} = (30 + 1)^{3} = 30^{3}+3*30^{2}*1 +3*30*1^{2} + 1^{3} = \ =27000 + 2700 + 90 + 1 = 29 791 \")
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![4) \ (x -6m)^{2}= x^{2} -12mx + 36m^{2} \ (5a +2)^{3}= (5a)^{3} + 3*(5a)^{2}*2 + 3*(5a)*2^{2} + 2^{3} = \ =125a^{3}+30a^{2}+60a + 8 \ (p^{3}g-3r^{2})(p^{3}g+3r^{2}) =( p^{3}g)^{2} - ( 3r^{2})^{2} = p^{6}g^{2} - 9r^{4} \ 5) \ x^{2}-18x + 60 = x^{2}- 2*9*x + 9^{2} - 9^{2} + 60 = \ = (x^{2}- 2*9*x + 9^{2}) - 9^{2} + 60 = (x- 9)^{2} - 81 + 60 = (x- 9)^{2} -21 \](https://tex.z-dn.net/?f=4%29+%5C+%28x+-6m%29%5E%7B2%7D%3D+x%5E%7B2%7D+-12mx+%2B+36m%5E%7B2%7D+%5C+%285a+%2B2%29%5E%7B3%7D%3D+%285a%29%5E%7B3%7D+%2B+3%2A%285a%29%5E%7B2%7D%2A2+%2B+3%2A%285a%29%2A2%5E%7B2%7D+%2B+2%5E%7B3%7D+%3D+%5C+%3D125a%5E%7B3%7D%2B30a%5E%7B2%7D%2B60a+%2B+8+%5C+%28p%5E%7B3%7Dg-3r%5E%7B2%7D%29%28p%5E%7B3%7Dg%2B3r%5E%7B2%7D%29+%3D%28+p%5E%7B3%7Dg%29%5E%7B2%7D+-+%28+3r%5E%7B2%7D%29%5E%7B2%7D+%3D+p%5E%7B6%7Dg%5E%7B2%7D+-+9r%5E%7B4%7D+%5C+5%29+%5C+x%5E%7B2%7D-18x+%2B+60+%3D+x%5E%7B2%7D-+2%2A9%2Ax+%2B+9%5E%7B2%7D+-+9%5E%7B2%7D+%2B+60+%3D+%5C+%3D+%28x%5E%7B2%7D-+2%2A9%2Ax+%2B+9%5E%7B2%7D%29+-+9%5E%7B2%7D+%2B+60+%3D+%28x-+9%29%5E%7B2%7D+-+81+%2B+60+%3D+%28x-+9%29%5E%7B2%7D+-21+%5C+ "4) \ (x -6m)^{2}= x^{2} -12mx + 36m^{2} \ (5a +2)^{3}= (5a)^{3} + 3*(5a)^{2}*2 + 3*(5a)*2^{2} + 2^{3} = \ =125a^{3}+30a^{2}+60a + 8 \ (p^{3}g-3r^{2})(p^{3}g+3r^{2}) =( p^{3}g)^{2} - ( 3r^{2})^{2} = p^{6}g^{2} - 9r^{4} \ 5) \ x^{2}-18x + 60 = x^{2}- 2*9*x + 9^{2} - 9^{2} + 60 = \ = (x^{2}- 2*9*x + 9^{2}) - 9^{2} + 60 = (x- 9)^{2} - 81 + 60 = (x- 9)^{2} -21 \")
Далее..........
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