Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{14y}\color{blue}{+3})(\color{red}{-14y}\color{blue}{+3})=\color{blue}{3}^2-\color{red}{(14y)}^2=9-196y^2\)
2. \((4s^4+7)(4s^4+7)=(4s^4+7)^2=(4s^4)^2\color{magenta}{+2.(4s^4).7}+7^2=16s^{8}\color{magenta}{+56s^4}+49\)
3. \((\color{red}{-14y}\color{blue}{+4})(\color{red}{14y}\color{blue}{+4})=\color{blue}{4}^2-\color{red}{(14y)}^2=16-196y^2\)
4. \((-16s^3+2q)^2=(-16s^3)^2\color{magenta}{+2.(-16s^3).(2q)}+(2q)^2=256s^{6}\color{magenta}{-64qs^3}+4q^2\)
5. \((q+7)^2=q^2+\color{magenta}{2.q.7}+7^2=q^2\color{magenta}{+14q}+49\)
6. \((-9p^2-12)(-9p^2-12)=(-9p^2-12)^2=(-9p^2)^2\color{magenta}{+2.(-9p^2).(-12)}+(-12)^2=81p^{4}\color{magenta}{+216p^2}+144\)
7. \((\color{red}{15s^4}\color{blue}{+16a})(\color{red}{-15s^4}\color{blue}{+16a})=\color{blue}{(16a)}^2-\color{red}{(15s^4)}^2=256a^2-225s^{8}\)
8. \((11x^4+16)(11x^4+16)=(11x^4+16)^2=(11x^4)^2\color{magenta}{+2.(11x^4).16}+16^2=121x^{8}\color{magenta}{+352x^4}+256\)
9. \((-7p+9)^2=(-7p)^2+\color{magenta}{2.(-7p).9}+9^2=49p^2\color{magenta}{-126p}+81\)
10. \((a+9)^2=a^2+\color{magenta}{2.a.9}+9^2=a^2\color{magenta}{+18a}+81\)
11. \((-4p-1)(-4p-1)=(-4p-1)^2=(-4p)^2+\color{magenta}{2.(-4p).(-1)}+(-1)^2=16p^2\color{magenta}{+8p}+1\)
12. \((\color{blue}{-16b^2}\color{red}{-16y})(\color{blue}{-16b^2}\color{red}{+16y})=\color{blue}{(-16b^2)}^2-\color{red}{(-16y)}^2=256b^{4}-256y^2\)