Question

•Factorise:

(a) 14m5n4p2 - 42m7n3p7 - 70m6n4p3 (b) 2a2(b2 - c2) + b2(2c2 - 2a2) + 2c2(a2 - b2)

•The area of a rectangle is 6a2 + 36a and 36a width.

Find the length of the rectangle.

•What are the common factors of the following terms?

(a) 25x2y, 30xy2 (b) 63m3n, 54mn4​

Answer 1

Answer:

a2 + b2 + c2 – ab – bc – ca = 0

Multiply both sides with 2, we get

2( a2 + b2 + c2 – ab – bc – ca) = 0

⇒ 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0

⇒ a2 + a2 + b2 + b2 + c2 + c2– 2ab – 2bc – 2ca = 0

⇒ (a2 – 2ab + b2) + (b2 – 2bc + c2) + (c2 – 2ca + a2) = 0

⇒ (a – b)2 + (b – c)2 + (c – a)2 = 0

Since the sum of squares is zero, it means each term should be zero.

⇒ (a – b)2 = 0, (b – c)2 = 0, (c – a)2 = 0

⇒ a – b = 0, b – c = 0, c – a = 0

⇒ a = b, b = c, c = a

⇒ a = b = c

Put this value in the equation ,

a/b+c +b/c+a +c/b+a =3/2

Hope this will help

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Answer 2

Answer:

(a) 14m5n4p2 - 42m7n3p7 - 70m6n4p3 (b) 2a2(b2 - c2) + b2(2c2 - 2a2) + 2c2(a2 - b2)

•The area of a rectangle is 6a2 + 36a and 36a width.

Find the length of the rectangle.

•What are the common factors of the following terms?

(a) 25x2y, 30xy2 (b) 63m3n, 54mn4