Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

1. \((11b^2-11)(-11b^2-11)\)
2. \((3s^5+13)^2\)
3. \((15q^2+16x)^2\)
4. \((-10q^2-14a)^2\)
5. \((9x^5-8)^2\)
6. \((-10a^2-15)(10a^2-15)\)
7. \((-5a^4-8s)(-5a^4-8s)\)
8. \((12y^2+8)^2\)
9. \((15p^5+13)(-15p^5+13)\)
10. \((2y-7)(-2y-7)\)
11. \((2x^2+9s)(2x^2-9s)\)
12. \((9y+13)(-9y+13)\)

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((\color{red}{11b^2}\color{blue}{-11})(\color{red}{-11b^2}\color{blue}{-11})=\color{blue}{(-11)}^2-\color{red}{(11b^2)}^2=121-121b^{4}\)
2. \((3s^5+13)^2=(3s^5)^2\color{magenta}{+2.(3s^5).13}+13^2=9s^{10}\color{magenta}{+78s^5}+169\)
3. \((15q^2+16x)^2=(15q^2)^2\color{magenta}{+2.(15q^2).(16x)}+(16x)^2=225q^{4}\color{magenta}{+480q^2x}+256x^2\)
4. \((-10q^2-14a)^2=(-10q^2)^2\color{magenta}{+2.(-10q^2).(-14a)}+(-14a)^2=100q^{4}\color{magenta}{+280aq^2}+196a^2\)
5. \((9x^5-8)^2=(9x^5)^2\color{magenta}{+2.(9x^5).(-8)}+(-8)^2=81x^{10}\color{magenta}{-144x^5}+64\)
6. \((\color{red}{-10a^2}\color{blue}{-15})(\color{red}{10a^2}\color{blue}{-15})=\color{blue}{(-15)}^2-\color{red}{(10a^2)}^2=225-100a^{4}\)
7. \((-5a^4-8s)(-5a^4-8s)=(-5a^4-8s)^2=(-5a^4)^2\color{magenta}{+2.(-5a^4).(-8s)}+(-8s)^2=25a^{8}\color{magenta}{+80a^4s}+64s^2\)
8. \((12y^2+8)^2=(12y^2)^2\color{magenta}{+2.(12y^2).8}+8^2=144y^{4}\color{magenta}{+192y^2}+64\)
9. \((\color{red}{15p^5}\color{blue}{+13})(\color{red}{-15p^5}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(15p^5)}^2=169-225p^{10}\)
10. \((\color{red}{2y}\color{blue}{-7})(\color{red}{-2y}\color{blue}{-7})=\color{blue}{(-7)}^2-\color{red}{(2y)}^2=49-4y^2\)
11. \((\color{blue}{2x^2}\color{red}{+9s})(\color{blue}{2x^2}\color{red}{-9s})=\color{blue}{(2x^2)}^2-\color{red}{(9s)}^2=4x^{4}-81s^2\)
12. \((\color{red}{9y}\color{blue}{+13})(\color{red}{-9y}\color{blue}{+13})=\color{blue}{13}^2-\color{red}{(9y)}^2=169-81y^2\)