Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((15a^3+1)(15a^3+1)\)
2. \((s-10)^2\)
3. \((s+4)^2\)
4. \((-9y-1)(-9y+1)\)
5. \((-p^2+15b)^2\)
6. \((-14p+11)(-14p+11)\)
7. \((s-1)^2\)
8. \((4p^2+6)(4p^2+6)\)
9. \((b-6)(b-6)\)
10. \((-12s^3+8y)(-12s^3+8y)\)
11. \((p+12)(p+12)\)
12. \((-9y^4-5)(-9y^4+5)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15a^3+1)(15a^3+1)=(15a^3+1)^2=(15a^3)^2\color{magenta}{+2.(15a^3).1}+1^2=225a^{6}\color{magenta}{+30a^3}+1\)
2. \((s-10)^2=s^2+\color{magenta}{2.s.(-10)}+(-10)^2=s^2\color{magenta}{-20s}+100\)
3. \((s+4)^2=s^2+\color{magenta}{2.s.4}+4^2=s^2\color{magenta}{+8s}+16\)
4. \((\color{blue}{-9y}\color{red}{-1})(\color{blue}{-9y}\color{red}{+1})=\color{blue}{(-9y)}^2-\color{red}{(-1)}^2=81y^2-1\)
5. \((-p^2+15b)^2=(-p^2)^2\color{magenta}{+2.(-p^2).(15b)}+(15b)^2=p^{4}\color{magenta}{-30bp^2}+225b^2\)
6. \((-14p+11)(-14p+11)=(-14p+11)^2=(-14p)^2+\color{magenta}{2.(-14p).11}+11^2=196p^2\color{magenta}{-308p}+121\)
7. \((s-1)^2=s^2+\color{magenta}{2.s.(-1)}+(-1)^2=s^2\color{magenta}{-2s}+1\)
8. \((4p^2+6)(4p^2+6)=(4p^2+6)^2=(4p^2)^2\color{magenta}{+2.(4p^2).6}+6^2=16p^{4}\color{magenta}{+48p^2}+36\)
9. \((b-6)(b-6)=(b-6)^2=b^2+\color{magenta}{2.b.(-6)}+(-6)^2=b^2\color{magenta}{-12b}+36\)
10. \((-12s^3+8y)(-12s^3+8y)=(-12s^3+8y)^2=(-12s^3)^2\color{magenta}{+2.(-12s^3).(8y)}+(8y)^2=144s^{6}\color{magenta}{-192s^3y}+64y^2\)
11. \((p+12)(p+12)=(p+12)^2=p^2+\color{magenta}{2.p.12}+12^2=p^2\color{magenta}{+24p}+144\)
12. \((\color{blue}{-9y^4}\color{red}{-5})(\color{blue}{-9y^4}\color{red}{+5})=\color{blue}{(-9y^4)}^2-\color{red}{(-5)}^2=81y^{8}-25\)