Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((15x^4-7)^2=(15x^4)^2\color{magenta}{+2.(15x^4).(-7)}+(-7)^2=225x^{8}\color{magenta}{-210x^4}+49\)
2. \((\color{blue}{x}\color{red}{-15})(\color{blue}{x}\color{red}{+15})=\color{blue}{x}^2-\color{red}{15}^2=x^2-225\)
3. \((\color{red}{-2b^2}\color{blue}{+16})(\color{red}{2b^2}\color{blue}{+16})=\color{blue}{16}^2-\color{red}{(2b^2)}^2=256-4b^{4}\)
4. \((p-3)(p-3)=(p-3)^2=p^2+\color{magenta}{2.p.(-3)}+(-3)^2=p^2\color{magenta}{-6p}+9\)
5. \((-9y^4+10x)(-9y^4+10x)=(-9y^4+10x)^2=(-9y^4)^2\color{magenta}{+2.(-9y^4).(10x)}+(10x)^2=81y^{8}\color{magenta}{-180xy^4}+100x^2\)
6. \((\color{blue}{q}\color{red}{-2})(\color{blue}{q}\color{red}{+2})=\color{blue}{q}^2-\color{red}{2}^2=q^2-4\)
7. \((\color{red}{-10b^2}\color{blue}{-11s})(\color{red}{10b^2}\color{blue}{-11s})=\color{blue}{(-11s)}^2-\color{red}{(10b^2)}^2=121s^2-100b^{4}\)
8. \((\color{red}{16x}\color{blue}{+2})(\color{red}{-16x}\color{blue}{+2})=\color{blue}{2}^2-\color{red}{(16x)}^2=4-256x^2\)
9. \((\color{red}{2x^3}\color{blue}{+7b})(\color{red}{-2x^3}\color{blue}{+7b})=\color{blue}{(7b)}^2-\color{red}{(2x^3)}^2=49b^2-4x^{6}\)
10. \((b+4)^2=b^2+\color{magenta}{2.b.4}+4^2=b^2\color{magenta}{+8b}+16\)
11. \((9x^2+9)^2=(9x^2)^2\color{magenta}{+2.(9x^2).9}+9^2=81x^{4}\color{magenta}{+162x^2}+81\)
12. \((-13q^3-2s)(-13q^3-2s)=(-13q^3-2s)^2=(-13q^3)^2\color{magenta}{+2.(-13q^3).(-2s)}+(-2s)^2=169q^{6}\color{magenta}{+52q^3s}+4s^2\)