\(1,a,=16x^2+24xy+9y^2\\ b,=4x^9-\dfrac{4}{5}x^3y+\dfrac{1}{25}y^2\\ c,=\left(2x-5y\right)\left(2x+5y\right)\\ d,=\left(11x-6y^2\right)\left(11x+6y^2\right)\\ 2,a,=\left(3x-1\right)^2\\ b,=-\left(-18x+x^2+81\right)=-\left(x-9\right)^2\\ c,=\left(x^2-4y^2\right)\\ d,=\left(25x^2-\dfrac{1}{9}y^2\right)\)
1.
\(a.\left(4x+3y\right)^2=16x^2+24xy+9y^2\)
\(b.\left(2x^3-\dfrac{1}{5}y\right)^2=4x^5-\dfrac{4}{5}x^3y+\dfrac{1}{25}y^2\)
\(c.4x^2-25y^2=\left(2x+5y\right)\left(2x-5y\right)\)
\(d.121x^2-36y^4=\left(11x+6y^2\right)\left(11x-6y^2\right)\)
2.
\(a.-6x+9x^2+1=\left(3x\right)^2-6x+1=\left(3x-1\right)^2\)
\(b.18x-x^2-81=-\left(x^2-18x+81\right)=-\left(x-9\right)^2\)
\(c.\left(x+2y\right)\left(x-2y\right)=x^2-4y^2\)
\(d.\left(5x-\dfrac{1}{3}y\right)\left(\dfrac{1}{3}y+5x\right)=\left(5x-\dfrac{1}{3}y\right)\left(5x+\dfrac{1}{3}y\right)=25x^2-\dfrac{1}{9}y^2\)
3.
\(a.96^2=\left(100-4\right)^2=10000-800+16=9216\)
\(b.103.97=\left(100+3\right)\left(100-3\right)=10000-9=9991\)
4.
\(\left(x+2y\right)\left(x-4\right)-\left(2x+1\right)\left(y-7\right)-x\left(y+5\right)\)
\(=x^2-4x+2xy-8y-2xy+14x-y+7-xy-5x\)
\(=x^2+5x-xy-9y+7\)
\(=\left(-1\right)^2+5.\left(-1\right)-2.\left(-1\right)-9.2+7=-13\)
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