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k305
@k305
December 2021
1
20
Report
ЗНАТОКИ!! СРОЧНО, ПОМОГИТЕ!!
Преобразуйте в многочлен выражение:
1. (а-б)^2(а+б)
2. (а+2б)^2(а-2б)
3. 7с(4с+2)-(7+с)^2
4. (б+4)^2-2б(5б+4)
5. (б-2)^2-2б(6б-2)
6. -3с(6с+2)-(-3+с)^2
7. (-8x+5y)^2-16x(-8x-5y)
8. y(7y+4x)-(2x+y)^2
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Answers & Comments
Genevra21
1.
(
a−b
)^
2
(
a+b
)
=
(
a^2
−2ab+
b^2)
(
a+b
)
=
a^3
+
a^2
b−2
a^2
b−2a
b^2
+
b^2
a+
b^3
=
a^3
−
a^2
b−a
b^2
+
b^3;
2.
(
a+2b
)^
2
(
a−2b
)
=
(
a^2
+4ab+4
b^2
)
(
a−2b
)
=
a^3-2
a^2
b+4
a^2
b−8a
b^2
+4
b^2
a−8
b^3
=
a^3
+2
a^2
b−4a
b^2
−8
b^3;
3.
7c
(
4c+2
)
−
(
7+c
)^
2
=28
c^2
+14c−49−14c−
c^2
=27
c^2
−
49;
4.
(
b+4
)^
2
−2b
(
5b+4
)
=
b^2
+8b+16−10
b^2
−8b=−9
b^2
+
16;
5.
(
b−2
)^
2
−2b
(
6b−2
)=
b^2
−4b+4−12
b^2
+4b=
−11
b^2
+4;
6.
−3c
(
6c+2
)
−
(
−3+c
)^
2
=−18
c^2
−6c−9+6c−
c^2
=−19
c^2
−9;7.(−8x+5y)^2−16x(−8x−5y)=64x^2−80xy+25y^2+128x^2+80xy= 192x^2+25y^2;
8.y(7y+4x)−(2x+y)^2=7y^2+4xy−4x^2−4xy−y^2=6y^2−4x^2.
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Answers & Comments
2.(a+2b)^2(a−2b)=(a^2+4ab+4b^2)(a−2b)=a^3-2a^2b+4a^2b−8ab^2+4b^2a−8b^3=a^3+2a^2b−4ab^2−8b^3;
3.7c(4c+2)−(7+c)^2=28c^2+14c−49−14c−c^2=27c^2−49;
4.(b+4)^2−2b(5b+4)=b^2+8b+16−10b^2−8b=−9b^2+16;
5.(b−2)^2−2b(6b−2)=b^2−4b+4−12b^2+4b=−11b^2+4;
6.−3c(6c+2)−(−3+c)^2=−18c^2−6c−9+6c−c^2=−19c^2−9;7.(−8x+5y)^2−16x(−8x−5y)=64x^2−80xy+25y^2+128x^2+80xy= 192x^2+25y^2;
8.y(7y+4x)−(2x+y)^2=7y^2+4xy−4x^2−4xy−y^2=6y^2−4x^2.