Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((x+2)^2=(x)^2+\color{magenta}{2.(x).2}+2^2=x^2\color{magenta}{+4x}+4\)
2. \((a-10)(a-10)=(a-10)^2=a^2+\color{magenta}{2.a.(-10)}+(-10)^2=a^2\color{magenta}{-20a}+100\)
3. \((\color{blue}{-4s^4}\color{red}{-7q})(\color{blue}{-4s^4}\color{red}{+7q})=\color{blue}{(-4s^4)}^2-\color{red}{(-7q)}^2=16s^{8}-49q^2\)
4. \((\color{blue}{-8y}\color{red}{-12})(\color{blue}{-8y}\color{red}{+12})=\color{blue}{(-8y)}^2-\color{red}{(-12)}^2=64y^2-144\)
5. \((\color{blue}{y}\color{red}{-4})(\color{blue}{y}\color{red}{+4})=\color{blue}{y}^2-\color{red}{4}^2=y^2-16\)
6. \((\color{red}{14s^5}\color{blue}{+12})(\color{red}{-14s^5}\color{blue}{+12})=\color{blue}{12}^2-\color{red}{(14s^5)}^2=144-196s^{10}\)
7. \((-3b^4-10y)^2=(-3b^4)^2\color{magenta}{+2.(-3b^4).(-10y)}+(-10y)^2=9b^{8}\color{magenta}{+60b^4y}+100y^2\)
8. \((-2b+16)^2=(-2b)^2+\color{magenta}{2.(-2b).16}+16^2=4b^2\color{magenta}{-64b}+256\)
9. \((12b+12)(12b+12)=(12b+12)^2=(12b)^2+\color{magenta}{2.(12b).12}+12^2=144b^2\color{magenta}{+288b}+144\)
10. \((-10a^4+8x)^2=(-10a^4)^2\color{magenta}{+2.(-10a^4).(8x)}+(8x)^2=100a^{8}\color{magenta}{-160a^4x}+64x^2\)
11. \((6x^4-7)^2=(6x^4)^2\color{magenta}{+2.(6x^4).(-7)}+(-7)^2=36x^{8}\color{magenta}{-84x^4}+49\)
12. \((\color{red}{6y}\color{blue}{+11})(\color{red}{-6y}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(6y)}^2=121-36y^2\)