Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((13x^4+10a)(13x^4+10a)=(13x^4+10a)^2=(13x^4)^2\color{magenta}{+2.(13x^4).(10a)}+(10a)^2=169x^{8}\color{magenta}{+260ax^4}+100a^2\)
2. \((\color{blue}{q}\color{red}{-11})(\color{blue}{q}\color{red}{+11})=\color{blue}{q}^2-\color{red}{11}^2=q^2-121\)
3. \((12y-10)^2=(12y)^2+\color{magenta}{2.(12y).(-10)}+(-10)^2=144y^2\color{magenta}{-240y}+100\)
4. \((13p^4-7)(13p^4-7)=(13p^4-7)^2=(13p^4)^2\color{magenta}{+2.(13p^4).(-7)}+(-7)^2=169p^{8}\color{magenta}{-182p^4}+49\)
5. \((\color{blue}{-11p^4}\color{red}{-16})(\color{blue}{-11p^4}\color{red}{+16})=\color{blue}{(-11p^4)}^2-\color{red}{(-16)}^2=121p^{8}-256\)
6. \((q-11)(q-11)=(q-11)^2=q^2+\color{magenta}{2.q.(-11)}+(-11)^2=q^2\color{magenta}{-22q}+121\)
7. \((\color{blue}{p}\color{red}{+1})(\color{blue}{p}\color{red}{-1})=\color{blue}{p}^2-\color{red}{1}^2=p^2-1\)
8. \((\color{blue}{y}\color{red}{-4})(\color{blue}{y}\color{red}{+4})=\color{blue}{(y)}^2-\color{red}{(-4)}^2=y^2-16\)
9. \((\color{red}{-q^5}\color{blue}{-13x})(\color{red}{q^5}\color{blue}{-13x})=\color{blue}{(-13x)}^2-\color{red}{(q^5)}^2=169x^2-q^{10}\)
10. \((\color{blue}{11y^5}\color{red}{+2})(\color{blue}{11y^5}\color{red}{-2})=\color{blue}{(11y^5)}^2-\color{red}{2}^2=121y^{10}-4\)
11. \((-16y^3+13)^2=(-16y^3)^2\color{magenta}{+2.(-16y^3).13}+13^2=256y^{6}\color{magenta}{-416y^3}+169\)
12. \((\color{blue}{15a}\color{red}{-10})(\color{blue}{15a}\color{red}{+10})=\color{blue}{(15a)}^2-\color{red}{(-10)}^2=225a^2-100\)