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a) ta có : \(M=\left(a+b\right)^3+2a^2+4ab+2b^2\)
\(M=\left(a+b\right)^3+2\left(a^2+2ab+b^2\right)=\left(a+b\right)^3+2\left(a+b\right)^2\)
\(M=\left(7\right)^3+2.\left(7\right)^2=343+98=441\) vậy \(M=441\) khi \(a+b=7\)
b) ta có : \(N=\left(a-b\right)^3-a^2+2ab-b^2\)
\(N=\left(a-b\right)^3-\left(a^2-2ab+b^2\right)=\left(a-b\right)^3-\left(a-b\right)^2\)
\(N=\left(5\right)^3-\left(5\right)^2=125-25=100\) vậy \(N=100\) khi \(a-b=5\)
c) ta có : \(\left(a-b\right)^2=a^2-2ab+b^2=a^2+2ab+b^2-4ab\)
\(=\left(a+b\right)^2-4ab=\left(5\right)^2-4.2=25-8=17\)
vậy \(\left(a-b\right)^2=17\) khi \(a+b=5\) và \(ab=2\)
a) \(4a^2b^2-c^2d^2\)
\(=\left(2ab\right)^2-\left(cd\right)^2\)
\(=\left(2ab-cd\right)\left(2ab+cd\right)\)
b) \(\left(a^2+2a+3\right)\left(a^2+2a-3\right)\)
\(=\left(\left(a^2+2a\right)+3\right)\left(\left(a^2+2a\right)-3\right)\)
\(=\left(a^2+2a\right)^2-3^2\)
\(=\left(a^4+2a^2\right)-9\)
Ủng hộ nha
Thanks
a)\(\left(a+b\right)^2-\left(a-b\right)^2=\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)=2ab+2ab=4ab\)
b)\(\left(a+b\right)^3-\left(a-b\right)^3-2b^3=\left(a^3+b^3+3ab\left(a+b\right)\right)-\left(a^3-b^3-3ab\left(a-b\right)\right)-2b^3\)
\(2b^3-2b^3+3ab^2+3ab^2=6ab^2\)
a) \(9\left(a+b\right)^2-4\left(a-2b\right)^2\)
\(=\left[3\left(a+b\right)+2\left(a-2b\right)\right]\left[3\left(a+b\right)-2\left(a-2b\right)\right]\)
\(=\left(3a+3b+2a-4b\right)\left(3a+3b-2a+4b\right)\)
\(=\left(5a-b\right)\left(a+7b\right)\)
b) \(\left(2a-b\right)^2-4\left(a-b\right)^2\)
\(=\left[\left(2a-b\right)-2\left(a-b\right)\right]\left[\left(2a-b\right)+2\left(a-b\right)\right]\)
\(=\left(2a-b-2a+2b\right)\left(2a-b+2a-2b\right)\)
\(=b\left(4a-3b\right)\)
c) \(125-\left(x+2\right)^3\)
\(=\left(5-x-2\right)\left[25+5\left(x+2\right)+\left(x+2\right)^2\right]\)
\(=\left(3-x\right)\left(25+5x+10+x^2+4x+4\right)\)
\(=\left(3-x\right)\left(x^2+9x+39\right)\)
d) \(\left(x+3\right)^3-8=\left(x+3-2\right)\left[\left(x+3\right)^2+2\left(x+3\right)+4\right]\)
\(=\left(x+1\right)\left(x^2+8x+19\right)\)
e) \(x^{12}-y^4=\left(x^6\right)^2-\left(y^2\right)^2=\left(x^6-y^2\right)\left(x^6+y^2\right)\) 9 khai triển tiếp hđt 6,7)
Gọi
( a + b )2 = c
( a - b )2 = d
= c2 - d2
Áp dụng hằng đẳng thức số a2 - b2 = ( a + b ) ( a - b ) ta có :
c2 - d2
= ( c - d ) ( c + d )
= [ ( a +b ) - ( a - b ) ] . [ ( a + b ) - ( a - b ) ]
= 2a . 2b
= 4ab
Study well
bn giải thích tại sao lại bằng 2a.2b zậy?