Factorise:(i)4x^2+ 20x + 25 (ii) 16x^2 + 4y^2 + 9z^2 -16xy -12yz + 24xz
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Answer:
i)25−4x
2
−12xy−9y
2
=25−(4x
2
+12xy+9y
2
)
=5
2
−((2x)
2
+2×2x×3y+(3y)
2
)
=5
2
−(2x+3y)
2
=(5+2x+3y)(5−(2x+3y))
=(5+2x+3y)(5−2x−3y)
ii)x
2
−a
2
+10ab−25b
2
=x
2
−(a
2
−10ab+25b
2
)
=x
2
−(a
2
−2×a×5b+(5b)
2
)
=x
2
−(a−5b)
2
=(x+a−5b)(x−(a−5b))
=(x+a−5b)(x−a+5b)
iii)6xy+x
2
+9y
2
−4a
2
=(2×x×3y+x
2
+(3y)
2
)−(2a)
2
=(x+3y)
2
−(2a)
2
=(x+3y+2a)(x+3y−2a)
iv)9x
2
+4+12x−a
2
+2ab−b
2
=((3x)
2
+(2
2
)+2×3x×2)−(a
2
−2ab+b
2
)
=(3x+2)
2
−(a−b)
2
=(3x+2+a−b)(3x+2−(a−b))
=(3x+2+a−b)(3x+2−a+b
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