Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((-14a^3+8x)(14a^3+8x)\)
2. \((a-3)(a+3)\)
3. \((-4q+12)(4q+12)\)
4. \((15a^2+16p)(15a^2+16p)\)
5. \((9b^2+3q)^2\)
6. \((-5y^4-8s)(-5y^4+8s)\)
7. \((-3y+9)(3y+9)\)
8. \((15y^4+2)^2\)
9. \((12p-13)(12p-13)\)
10. \((p+8)^2\)
11. \((-9a^2+12p)(-9a^2-12p)\)
12. \((b+1)(b+1)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{-14a^3}\color{blue}{+8x})(\color{red}{14a^3}\color{blue}{+8x})=\color{blue}{(8x)}^2-\color{red}{(14a^3)}^2=64x^2-196a^{6}\)
2. \((\color{blue}{a}\color{red}{-3})(\color{blue}{a}\color{red}{+3})=\color{blue}{a}^2-\color{red}{3}^2=a^2-9\)
3. \((\color{red}{-4q}\color{blue}{+12})(\color{red}{4q}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(4q)}^2=144-16q^2\)
4. \((15a^2+16p)(15a^2+16p)=(15a^2+16p)^2=(15a^2)^2\color{magenta}{+2.(15a^2).(16p)}+(16p)^2=225a^{4}\color{magenta}{+480a^2p}+256p^2\)
5. \((9b^2+3q)^2=(9b^2)^2\color{magenta}{+2.(9b^2).(3q)}+(3q)^2=81b^{4}\color{magenta}{+54b^2q}+9q^2\)
6. \((\color{blue}{-5y^4}\color{red}{-8s})(\color{blue}{-5y^4}\color{red}{+8s})=\color{blue}{(-5y^4)}^2-\color{red}{(-8s)}^2=25y^{8}-64s^2\)
7. \((\color{red}{-3y}\color{blue}{+9})(\color{red}{3y}\color{blue}{+9})=\color{blue}{9}^2-\color{red}{(3y)}^2=81-9y^2\)
8. \((15y^4+2)^2=(15y^4)^2\color{magenta}{+2.(15y^4).2}+2^2=225y^{8}\color{magenta}{+60y^4}+4\)
9. \((12p-13)(12p-13)=(12p-13)^2=(12p)^2+\color{magenta}{2.(12p).(-13)}+(-13)^2=144p^2\color{magenta}{-312p}+169\)
10. \((p+8)^2=p^2+\color{magenta}{2.p.8}+8^2=p^2\color{magenta}{+16p}+64\)
11. \((\color{blue}{-9a^2}\color{red}{+12p})(\color{blue}{-9a^2}\color{red}{-12p})=\color{blue}{(-9a^2)}^2-\color{red}{(12p)}^2=81a^{4}-144p^2\)
12. \((b+1)(b+1)=(b+1)^2=b^2+\color{magenta}{2.b.1}+1^2=b^2\color{magenta}{+2b}+1\)