Step-by-step explanation:
i) (b−7)
2
=b
+7
−2(b)(7)
+49−14b ∵[(a−b)
=a
+b
−2ab]
ii) (xy+3z)
=(xy)
+(3z)
+2(xy)(3z)
=x
y
+9z
+6xyz ∵[(a+b)
+2ab]
iii) (6x−5y)
=(6x)
+(5y)
−2(6x)(5y)
=36x
+25y
−60xy ∵[(a−b)
iv) (
3
m+
n)
=(
m)
+(
+2(
m)(
=
16
4
m
+
9
n
+2mn ∵[(a+b)
v) (0.4p−0.5q)
=(0.4p)
+(0.5q)
−2(0.4p)(0.5q)
=0.16p
+0.25q
−4pq ∵[(a−b)
vi) (2xy+5y)
=(2xy)
+2(2xy)(5y)
=4x
+20xy
∵[(a+b)
=y
(4x
+20x+25)
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Answers & Comments
Step-by-step explanation:
i) (b−7)
2
=b
2
+7
2
−2(b)(7)
=b
2
+49−14b ∵[(a−b)
2
=a
2
+b
2
−2ab]
ii) (xy+3z)
2
=(xy)
2
+(3z)
2
+2(xy)(3z)
=x
2
y
2
+9z
2
+6xyz ∵[(a+b)
2
=a
2
+b
2
+2ab]
iii) (6x−5y)
2
=(6x)
2
+(5y)
2
−2(6x)(5y)
=36x
2
+25y
2
−60xy ∵[(a−b)
2
=a
2
+b
2
−2ab]
iv) (
3
2
m+
2
3
n)
2
=(
3
2
m)
2
+(
2
3
n)
2
+2(
3
2
m)(
2
3
n)
=
16
4
m
2
+
4
9
n
2
+2mn ∵[(a+b)
2
=a
2
+b
2
+2ab]
v) (0.4p−0.5q)
2
=(0.4p)
2
+(0.5q)
2
−2(0.4p)(0.5q)
=0.16p
2
+0.25q
2
−4pq ∵[(a−b)
2
=a
2
+b
2
−2ab]
vi) (2xy+5y)
2
=(2xy)
2
+(5y)
2
+2(2xy)(5y)
=4x
2
y
2
+25y
2
+20xy
2
∵[(a+b)
2
=a
2
+b
2
+2ab]
=y
2
(4x
2
+20x+25)