Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{4x^3}\color{blue}{-12})(\color{red}{-4x^3}\color{blue}{-12})=\color{blue}{(-12)}^2-\color{red}{(4x^3)}^2=144-16x^{6}\)
2. \((\color{blue}{a}\color{red}{+14})(\color{blue}{a}\color{red}{-14})=\color{blue}{a}^2-\color{red}{14}^2=a^2-196\)
3. \((y+11)(y+11)=(y+11)^2=y^2+\color{magenta}{2.y.11}+11^2=y^2\color{magenta}{+22y}+121\)
4. \((10q^2+14)(10q^2+14)=(10q^2+14)^2=(10q^2)^2\color{magenta}{+2.(10q^2).14}+14^2=100q^{4}\color{magenta}{+280q^2}+196\)
5. \((\color{blue}{b^3}\color{red}{+13})(\color{blue}{b^3}\color{red}{-13})=\color{blue}{(b^3)}^2-\color{red}{13}^2=b^{6}-169\)
6. \((\color{red}{10s^3}\color{blue}{+2})(\color{red}{-10s^3}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(10s^3)}^2=4-100s^{6}\)
7. \((-5s+4)(-5s+4)=(-5s+4)^2=(-5s)^2+\color{magenta}{2.(-5s).4}+4^2=25s^2\color{magenta}{-40s}+16\)
8. \((\color{blue}{b}\color{red}{+9})(\color{blue}{b}\color{red}{-9})=\color{blue}{b}^2-\color{red}{9}^2=b^2-81\)
9. \((\color{red}{9y^5}\color{blue}{+2})(\color{red}{-9y^5}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(9y^5)}^2=4-81y^{10}\)
10. \((\color{red}{-13p^5}\color{blue}{-15x})(\color{red}{13p^5}\color{blue}{-15x})=\color{blue}{(-15x)}^2-\color{red}{(13p^5)}^2=225x^2-169p^{10}\)
11. \((x+15)^2=x^2+\color{magenta}{2.x.15}+15^2=x^2\color{magenta}{+30x}+225\)
12. \((q-3)^2=q^2+\color{magenta}{2.q.(-3)}+(-3)^2=q^2\color{magenta}{-6q}+9\)