Toán Lớp 8: 7. Tính nhanh a) $45^{2}+33^{2}-22^{2}+90.33$ b) $111^{2}-137^{2}-48^{2}+96.137$

Question

Toán Lớp 8:  7. Tính nhanh a)  $45^{2}+33^{2}-22^{2}+90.33$  b)  $111^{2}-137^{2}-48^{2}+96.137$

baoquyen · Answer

a, 45&sup2;+33&sup2;-22&sup2;+90.33   = (45&sup2;+2.45.33+33&sup2;)-22&sup2;   = (45+33)&sup2;-22&sup2;   = 78&sup2;-22&sup2;   = (78-22)(78+22)   = 56.100  = 5600   b, 111&sup2;-137&sup2;-48&sup2;+96.137   = 111&sup2;-(137&sup2;-2.48.137+48&sup2;)   = 111&sup2;-(137-48)&sup2;   = 111&sup2;-89&sup2;   = (111-89)(111+89)   = 22.200    = 4400

tuyetanhthu · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   a) $45^{2}+33^2-22^2+90.33$    =$45^{2}+2.45.33+33^2-22$    =$(45+33)^{2}-22^2$    =$78^{2}-22^2$    =$(78+22).(78-22)^{}$    =$100.56^{}$   =$5600^{}$    b) $111^{2}-137^2-48^2+96.137$    =$111^{2}-(137^2-2.48.137+48^2)$    =$111^{2}-(137-48)^2$    =$111^{2}-89^2$    =$(111+89).(111-89)^{}$    =$200.22^{}$    =$4400^{}$