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\(\left(3x\right)^2-42xy+49y^2=\left(3x-7y\right)^2\)
\(\left(3x+y\right)\left(3x-y\right)=9x^2-y^2\)
\(\left(5y-3x\right)\left(5y+3x\right)=25y^2-9x^2\)
a) x2+20x+*
=> x2 +2 x 5x2+52
= (x+5)2
b) 16x2+24xy+*
=> (4x)2+2 x 4x x 3+32
= (4x + 3)2
c) y2 -*+49
=> y2 - 2y72+72
= (y-7)2
d) * - 42xy + 49y2
= (3x)2 + 2 x 7y3x + (7y)2
= (3x+7y)2
a) x2 + 20x + *
= x2 + 2.x.10 + 102
= x2 + 20x + 100
b) 16x2 + 24xy +*
= 16x2 +2.x.12y + (12y)2
= 16x2 +24xy + 144y2
c) y2 - * + 49
= y2 - * +72
= y2 - 2.y.7 + 49
= y2 - 14y + 49
d) * - 42xy + 49y2
= * - 42xy + (7y)2
= * - 2.3x.7y + (7y)2
= (3x)2 - 42xy + (7y)2
= 9x2 - 42xy + 49y2
`a)x^2+20x+100=(x+10)^2`
`b)16x^2+24xy+9y^2=(4x+3y)^2`
`c)y^2-14y+49=(y-7)^2`
`d)9x^2-42xy+49y^2=(3x-7y)^2`
a, \(x^2+2x.10+100=\left(x+10\right)^2\)
\(b,16x^2+2.4x.3y+9y^2=\left(4x+3y\right)^2\)
\(c,y^2-14y+49=\left(y-7\right)^2\)
\(d,9x^2-2.3x.7x+49y^2=\left(3x-7y\right)^2\)
a.
$x^2+20x+100=(x+10)^2$
b.
$16x^2+24xy+9y^2=(4x+3y)^2$
c.
$y^2-14y+49=(y-7)^2$
d.
$9x^2-42xy+49y^2=(3x-7y)^2$
e.
$4x^2-9y^2=(2x-3y)(2x+3y)$
f.
$16-x^2=(4-x)(4+x)$
g.
$49x^2-1=(7x-1)(7x+1)$
h.
$16x^2-25=(4x-5)(4x+5)$
i.
$8x^3+24x^2y+54xy^2+27y^3=(2x+3y)^3$
k.
$x^3-6x^2y+12xy^2-8y^3=(x-2y)^3$
l.
$(2a+b)(4a^2-2ab+b^2)=(2a)^3+b^3=8a^3+b^3$
m.
$(3x-4y)(9x^2+12xy+16y^2)=(3x)^3-(4y)^3=27x^3-64y^3$
c: \(C=\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)\left(x+y-x+y\right)\)
=4xy
d: \(D=\left(\dfrac{x}{2}-y\right)\left(\dfrac{x}{2}+y\right)=\dfrac{1}{4}x^2-y^2\)
\(x^2+20x+100=\left(x+10\right)^2\)
\(16x^2+24xy+\left(3y\right)^2=\left(4x+3y\right)^2\)
\(y^2-14y+49=\left(y-7\right)^2\)
\(a,\) \(x^2+20x+100=\left(x+10\right)^2\)
\(b,\) \(16x^2+24x+9=\left(4x+3\right)^2\)
\(c,\) \(y^2-14x+49=\left(y-7\right)^2\)