Bài 3:
a) Ta có: \(\left(x+10\right)^2+\left(x-10\right)^2\)
\(=x^2+20x+100+x^2-20x+100\)
\(=2x^2+200\)
b) Ta có: \(\left(x-12\right)^2+\left(x+12\right)^2\)
\(=x^2-24x+144+x^2+24x+144\)
\(=2x^2+288\)
c) Ta có: \(\left(x+7\right)^2-\left(x-7\right)^2\)
\(=\left(x+7-x+7\right)\left(x+7+x-7\right)\)
\(=14\cdot2x\)
=28x
Bài 1:
a) Ta có: \(\left(a+12\right)^2\)
\(=a^2+2\cdot a\cdot12+12^2\)
\(=a^2+24a+144\)
b) Ta có: \(\left(3a+\dfrac{1}{3}\right)^2\)
\(=\left(3a\right)^2+2\cdot3a\cdot\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2\)
\(=9a^2+2a+\dfrac{1}{9}\)
c) Ta có: \(\left(5a^2+6\right)^2\)
\(=\left(5a^2\right)^2+2\cdot5a^2\cdot6+6^2\)
\(=25a^4+60a^2+36\)
d) Ta có: \(\left(\dfrac{1}{2}+4b\right)^2\)
\(=\left(\dfrac{1}{2}\right)^2+2\cdot\dfrac{1}{2}\cdot4b+\left(4b\right)^2\)
\(=\dfrac{1}{4}+4b+16b^2\)
e) Ta có: \(\left(a^m+b^n\right)^2\)
\(=\left(a^m\right)^2+2\cdot a^m\cdot b^n+\left(b^n\right)^2\)
\(=a^{2m}+2a^mb^n+b^{2n}\)
Bài 2:
a) Ta có: \(\left(x-0.3\right)^2\)
\(=x^2-2\cdot x\cdot0.3+0.3^2\)
\(=x^2-0.6x+0.9\)
b) Ta có: \(\left(6x-3y\right)^2\)
\(=\left(6x\right)^2-2\cdot6x\cdot3y+\left(3y\right)^2\)
\(=36x^2-36xy+9y^2\)
c) Ta có: \(\left(5-2xy\right)^2\)
\(=5^2-2\cdot5\cdot2xy+\left(2xy\right)^2\)
\(=4x^2y^2-20xy+25\)
d) Ta có: \(\left(x^4-1\right)^2\)
\(=\left(x^4\right)^2-2\cdot x^4\cdot1+1^2\)
\(=x^8-2x^4+1\)
e) Ta có: \(\left(x^5-y^3\right)^2\)
\(=\left(x^5\right)^2-2\cdot x^5y^3+\left(y^3\right)^2\)
\(=x^{10}-2x^5y^3+y^6\)
