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Dima0339
@Dima0339
July 2022
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ПОМОГИТЕ!СРОЧНО!АЛГЕБРА!!ПОЖАЛУЙСТА=(
ДАЮ 52 БАЛЛА
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oganesbagoyan
Verified answer
а)
(x+2)(3+x)(3-x) +x²(x+2) =(x+2)((3+x)(3-x) +x²) =(x+2)(3²-x² +x²) =9(x+2).
б)
(x+4)² -9(x-4)² =(x+4)² -(3(x-4))² =
(
(x+4) -3(x-4)
)(
(x+4)+3(x-4)) =
(x+4 -3x+12)(x+4 +3x -12) =(16 -2x)(4x-8) =2(8 -x)*4(x-2)=8(8-x)(x-2).
---------------
или (x+4)² -9(x-4)² =x² +8x+16 -9(x² -8x+16)=x² +8x+16 -9x² +72x-144 =- 8x²+80x -128=8(-x² +10x -16)=8(-x²+2x +8x -16) =8(-x(x-2) + 8(x-2)) =8(x-2)(8-x)
в)
2y4 +54y =2y(y³ +27) =2y(y³ +3³) =2y(y +3)(y² -3y+9).
г)
(x² -1)² +6(x² -1)+9 =(x² -1)² +2*(x² -1)*3+3² =(x² -1+3)² =(x² +2)² .
---------------
или (x²)² -2x²+1 +6x²-6 +9 =(x²)² +4x²+4 =(x²)² +2x²*2+2² =(x² +2)².
* * * x^4 +4x²+4 * * *
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Dima0339
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Verified answer
а) (x+2)(3+x)(3-x) +x²(x+2) =(x+2)((3+x)(3-x) +x²) =(x+2)(3²-x² +x²) =9(x+2).б)(x+4)² -9(x-4)² =(x+4)² -(3(x-4))² = ((x+4) -3(x-4))((x+4)+3(x-4)) =
(x+4 -3x+12)(x+4 +3x -12) =(16 -2x)(4x-8) =2(8 -x)*4(x-2)=8(8-x)(x-2).
---------------
или (x+4)² -9(x-4)² =x² +8x+16 -9(x² -8x+16)=x² +8x+16 -9x² +72x-144 =- 8x²+80x -128=8(-x² +10x -16)=8(-x²+2x +8x -16) =8(-x(x-2) + 8(x-2)) =8(x-2)(8-x)
в) 2y4 +54y =2y(y³ +27) =2y(y³ +3³) =2y(y +3)(y² -3y+9).
г) (x² -1)² +6(x² -1)+9 =(x² -1)² +2*(x² -1)*3+3² =(x² -1+3)² =(x² +2)² .
---------------
или (x²)² -2x²+1 +6x²-6 +9 =(x²)² +4x²+4 =(x²)² +2x²*2+2² =(x² +2)².
* * * x^4 +4x²+4 * * *