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\(=\left(3x+15\right)^2-\left(x-7\right)^2=\left(4x+8\right)\left(2x+22\right)=8\left(x+2\right)\left(x+11\right)\)
(x-7)^2 = x^2-14x+49
<=> 9x^2+90x+225 -x^2+14x-49
= 8x^2+104x+176
= 8(x^2+13+22)
<=> 8(x+2)(x+11)
9x2+90x+225-(x-7)2
=(3x+15)2-(x-7)2
=(3x+15-x+7)(3x+15+x-7)
=(2x+22)(4x+8)
=2 (x+11)4 (x+2)
=8 (x+11)(x+2)
9x2+90x+225-(x-7)2
=(3x)2+2.3x.15+152-(x-7)2
=(3x+15)2-(x-7)2
=[(3x+15)-(x-7)][(3x+15)+(x-7)]
=(3x+15-x+7)(3x+15+x-7)
=(2x+22)(4x+8)
=2(x+11).4(x+2)
=8(x+11)(x+2)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
\(x^8+3x^4+4\)
\(=\left(x^8-x^6+2x^4\right)+\left(x^6-x^4+2x^2\right)+\left(2x^4-2x^2+4\right)\)
\(=x^4\left(x^4-x^2+2\right)+x^2\left(x^4-x^2+2\right)+2\left(x^4-x^2+2\right)\)
\(=\left(x^4+x^2+2\right)\left(x^4-x^2+2\right)\)
\(4x^4+4x^3+5x^2+2x+1\)
\(=\left(4x^4+2x^3+2x^2\right)+\left(2x^3+x^2+x\right)+\left(2x^2+x+1\right)\)
\(=2x^2\left(2x^2+x+1\right)+x\left(2x^2+x+1\right)+\left(2x^2+x+1\right)\)
\(=\left(2x^2+x+1\right)^2\)
\(a,x^2\left(1-x^2\right)-4-4x^2\)
\(=x^2-x^4-4-4x^2\)
\(=x^2-\left(x^4+4x^2+4\right)\)
\(=x^2-\left(x^2+2\right)^2\)
\(=\left(2x^2+2\right).\left(-2\right)\)
\(=-4\left(x^2+1\right)\)
\(=x^4-9x^3+9x^3-81x^2-9x^2+81x+10x-90\)
\(=\left(x-9\right)\left(x^3+9x^2-9x+10\right)\)
\(=\left(x-9\right)\left(x^3+10x^2-x^2-10x+x+10\right)\)
\(=\left(x-9\right)\left(x+10\right)\left(x^2-x+1\right)\)