Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{y}\color{red}{+11})(\color{blue}{y}\color{red}{-11})=\color{blue}{y}^2-\color{red}{11}^2=y^2-121\)
2. \((8x^2+16)(8x^2+16)=(8x^2+16)^2=(8x^2)^2\color{magenta}{+2.(8x^2).16}+16^2=64x^{4}\color{magenta}{+256x^2}+256\)
3. \((-14q+6)(-14q+6)=(-14q+6)^2=(-14q)^2+\color{magenta}{2.(-14q).6}+6^2=196q^2\color{magenta}{-168q}+36\)
4. \((\color{red}{15x}\color{blue}{-14})(\color{red}{-15x}\color{blue}{-14})=\color{blue}{(-14)}^2-\color{red}{(15x)}^2=196-225x^2\)
5. \((-3s^5+9)(-3s^5+9)=(-3s^5+9)^2=(-3s^5)^2\color{magenta}{+2.(-3s^5).9}+9^2=9s^{10}\color{magenta}{-54s^5}+81\)
6. \((\color{red}{3y}\color{blue}{+10})(\color{red}{-3y}\color{blue}{+10})=\color{blue}{10}^2-\color{red}{(3y)}^2=100-9y^2\)
7. \((-3a^4+6)(-3a^4+6)=(-3a^4+6)^2=(-3a^4)^2\color{magenta}{+2.(-3a^4).6}+6^2=9a^{8}\color{magenta}{-36a^4}+36\)
8. \((x+5)(x+5)=(x+5)^2=x^2+\color{magenta}{2.x.5}+5^2=x^2\color{magenta}{+10x}+25\)
9. \((x^5+3p)^2=(x^5)^2\color{magenta}{+2.(x^5).(3p)}+(3p)^2=x^{10}\color{magenta}{+6px^5}+9p^2\)
10. \((s+7)^2=s^2+\color{magenta}{2.s.7}+7^2=s^2\color{magenta}{+14s}+49\)
11. \((\color{red}{-9q}\color{blue}{-13})(\color{red}{9q}\color{blue}{-13})=\color{blue}{(-13)}^2-\color{red}{(9q)}^2=169-81q^2\)
12. \((\color{blue}{y}\color{red}{+6})(\color{blue}{y}\color{red}{-6})=\color{blue}{y}^2-\color{red}{6}^2=y^2-36\)