Qisqa ko‘paytirish formulalari mavzusidan test savollari

Soddalashtiring:

(2a-b)^{2}-(2a+b)^{2}

Soddalashtiring:

(a-3b)^{2}-(a+b)^{2}

Ushbu (4x-3)^{2}-x(4x+1) ifodani ko‘phadining standart shakilga keltiring.

Soddalashtiring:

(1-2a)^{2}+(1+2a)(2a-1)

Ushbu (x-1)(2-x)+(2x-3)^{2} ifodani ko‘phadining standart shakilga keltiring.

Agar 5^{z}+5^{-z}=7 bo‘lsa, 25^{z}+25^{-z} ning qiymati qancha bo‘ladi?

Agar 49^{z}+49^{-z}=7 bo‘lsa, 7^{z}+7^{-z} ni toping.

-2a^{2}-2b^{2} ni a+b va ab orqali ifodalang.

(2k+1)^{2}-(2k-1)^{2} ifoda, k\in N da qaysi raqamlarga qoldiqsiz bo‘linadi?

Soddalashtiring:

12^{2}-(x+7)^{2}-(5-x)\cdot (19+x)

a^{2}+b^{2} ni ab va a+b orqali ifodalang.

\alpha va \beta irratsional sonlar (\alpha \ne \beta ), \alpha +\beta esa ratsional son. Quyidagilarning qaysi biri ratsional son bo‘ladi?

a=2^{5}+2^{-5} va b=2^{5}-2^{-5} bo‘lsa, a^{2}-b^{2} nimaga teng?

a^{2}+\frac{9}{a^{2}}=22 bo‘lsa a-\frac{3}{a} nimaga teng.

Ushbu (8+(2x-4))(8-(2x-4)) ifoda x ning qanday qiymatida eng kata qiymatga erishadi?

Ushbu (x^{2}-xy+y^{2})(x+y) ifodaning x=-\frac{1}{2} y=\frac{1}{\sqrt[3]{2}} bo‘lgandagi qiymatini hisoblang.

Ushbu (x^{4}-x^{2}y^{2}+y^{4})(x^{2}+y^{2}) ko‘paytma o‘xshash hadlari ixchamlanganidan keyin nechta qo‘shiluvchidan iborat bo‘ladi?

(b-c)(b^{2}+bc+c^{2}) ifodaning b=-2 va c=1 bo‘lgandagi qiymatini hisoblang.

(x^{2}+xy+y^{2})(x-y) ifodaning x=1 va y=-2 bo‘lgandagi qiymatini hisoblang.

Ushbu (y^{4}-y^{2}+1)(y^{2}+1)+(y-1)(y+1) ifodani soddalashtirgandan keyin hosil bo‘lgan ko‘phadning nechta hadi bo‘ladi?

(x^{2}+1)(x^{4}-x^{2}+1)+(x^{3}-1)^{2} ni soddalashtirgandan keyin hosil bo‘lgan ko‘phadning nechta hadi bo‘ladi?

Ifodani soddalashtirgandan keyin nechta haddan iborat bo‘ladi? (y^{3}-1)^{2}+(y^{2}+1)(y^{4}-y^{2}+1)

(2a+3b)(4a^{2}-6ab+9b^{2}) ifodaning a=2 va b=1 dagi qiymatini toping?

Hisoblang:

0.8\cdot (0.2+1)\cdot (0.2^{2}+1)\cdot (0.2^{4}+1)\cdot (0.2^{8}+1)+(5^{-2})^{8}

(x+3)(x^{2}-3x+9) ifodaning x=\frac{1}{2} dagi qiymatini hisoblang?

Agar a+\frac{1}{a}=3 bo‘lsa \frac{a^{6}+1}{a^{3}} ning qiymatini toping.

Agar a-\frac{1}{a}=\sqrt{7} bo‘lsa, a^{4}+\frac{1}{a^{4}} ning qiymatini hisoblang.

Agar a+\frac{1}{a}=3 bo‘lsa \frac{a^{4}+1}{2a^{2}} ning qiymati nimaga teng?

Agar a-\frac{1}{a}=\frac{2}{3} bo‘lsa \frac{a^{4}+1}{a^{2}} ning qiymatini toping?

Agar a+a^{-1}=3 bo‘lsa a^{2}+a^{-2} ni hisoblang?