Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{blue}{-x}\color{red}{+4})(\color{blue}{-x}\color{red}{-4})=\color{blue}{(-x)}^2-\color{red}{(4)}^2=x^2-16\)
2. \((-13s^2+3)(-13s^2+3)=(-13s^2+3)^2=(-13s^2)^2\color{magenta}{+2.(-13s^2).3}+3^2=169s^{4}\color{magenta}{-78s^2}+9\)
3. \((\color{red}{9q}\color{blue}{-11})(\color{red}{-9q}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(9q)}^2=121-81q^2\)
4. \((-5s^4+12y)^2=(-5s^4)^2\color{magenta}{+2.(-5s^4).(12y)}+(12y)^2=25s^{8}\color{magenta}{-120s^4y}+144y^2\)
5. \((\color{red}{10b^4}\color{blue}{-12x})(\color{red}{-10b^4}\color{blue}{-12x})=\color{blue}{(-12x)}^2-\color{red}{(10b^4)}^2=144x^2-100b^{8}\)
6. \((\color{red}{-10p}\color{blue}{+11})(\color{red}{10p}\color{blue}{+11})=\color{blue}{11}^2-\color{red}{(10p)}^2=121-100p^2\)
7. \((q+2)^2=q^2+\color{magenta}{2.q.2}+2^2=q^2\color{magenta}{+4q}+4\)
8. \((a+5)(a+5)=(a+5)^2=a^2+\color{magenta}{2.a.5}+5^2=a^2\color{magenta}{+10a}+25\)
9. \((s+7)^2=s^2+\color{magenta}{2.s.7}+7^2=s^2\color{magenta}{+14s}+49\)
10. \((x+8)(x+8)=(x+8)^2=x^2+\color{magenta}{2.x.8}+8^2=x^2\color{magenta}{+16x}+64\)
11. \((16a^2-13)^2=(16a^2)^2\color{magenta}{+2.(16a^2).(-13)}+(-13)^2=256a^{4}\color{magenta}{-416a^2}+169\)
12. \((b-2)^2=b^2+\color{magenta}{2.b.(-2)}+(-2)^2=b^2\color{magenta}{-4b}+4\)