Question

Find the HCF of the terms of the expression.

$2b^2c + 4b^4c^2 + 16b^2 c^2$
Alos, write the factors of the above expression.

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Answer 1

Step-by-step explanation:

Given : Expression 2b^3c+4b^3c^2+16bc^32b

3

c+4b

3

c

2

+16bc

3

To find : Find the HCF of the terms of the expression and also write the factors ?

Solution :

HCF is the highest common factors.

2b^3c=2\times b\times b\times b\times c2b

3

c=2×b×b×b×c

\begin{gathered}4b^3c^2=2\\times 2\times b\times b\times b\times c\times c\end{gathered}

4b

3

c

2

=2

times2×b×b×b×c×c

16bc^3=2\times2\times 2\times 2\times b\times c\times c\times c16bc

3

=2×2×2×2×b×c×c×c

The HCF is 2\times b\times c=2bc2×b×c=2bc

Expression 2b^3c+4b^3c^2+16bc^32b

3

c+4b

3

c

2

+16bc

3

Taking '2bc' common,

2bc(b^2+2b^2c+4c^2)2bc(b

2

+2b

2

c+4c

2

)

The factors are 2bc2bc and b^2+2b^2c+4c^2b

2

+2b

2

c+4c

2