Merkwaardige producten (MP)

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Bereken de volgende merkwaardige producten

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

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Bereken de volgende merkwaardige producten

Verbetersleutel

1. \((y+14)(y+14)=(y+14)^2=(y)^2+\color{magenta}{2.(y).14}+14^2=y^2\color{magenta}{+28y}+196\)
2. \((\color{red}{-14a^4}\color{blue}{+14b})(\color{red}{14a^4}\color{blue}{+14b})=\color{blue}{(14b)}^2-\color{red}{(14a^4)}^2=196b^2-196a^{8}\)
3. \((12x+7)^2=(12x)^2+\color{magenta}{2.(12x).7}+7^2=144x^2\color{magenta}{+168x}+49\)
4. \((\color{blue}{p}\color{red}{+7})(\color{blue}{p}\color{red}{-7})=\color{blue}{p}^2-\color{red}{7}^2=p^2-49\)
5. \((\color{red}{9s}\color{blue}{-3})(\color{red}{-9s}\color{blue}{-3})=\color{blue}{(-3)}^2-\color{red}{(9s)}^2=9-81s^2\)
6. \((\color{blue}{8x^3}\color{red}{-7})(\color{blue}{8x^3}\color{red}{+7})=\color{blue}{(8x^3)}^2-\color{red}{(-7)}^2=64x^{6}-49\)
7. \((\color{blue}{b}\color{red}{-4})(\color{blue}{b}\color{red}{+4})=\color{blue}{b}^2-\color{red}{4}^2=b^2-16\)
8. \((-6b^5+10q)(-6b^5+10q)=(-6b^5+10q)^2=(-6b^5)^2\color{magenta}{+2.(-6b^5).(10q)}+(10q)^2=36b^{10}\color{magenta}{-120b^5q}+100q^2\)
9. \((\color{red}{13y^3}\color{blue}{-10b})(\color{red}{-13y^3}\color{blue}{-10b})=\color{blue}{(-10b)}^2-\color{red}{(13y^3)}^2=100b^2-169y^{6}\)
10. \((\color{blue}{y}\color{red}{-1})(\color{blue}{y}\color{red}{+1})=\color{blue}{y}^2-\color{red}{1}^2=y^2-1\)
11. \((4s^5-12)^2=(4s^5)^2\color{magenta}{+2.(4s^5).(-12)}+(-12)^2=16s^{10}\color{magenta}{-96s^5}+144\)
12. \((\color{red}{15q^2}\color{blue}{+5y})(\color{red}{-15q^2}\color{blue}{+5y})=\color{blue}{(5y)}^2-\color{red}{(15q^2)}^2=25y^2-225q^{4}\)