Question

factorize ((m+2n)^2)(x^2)-22x(m+2n)+72

Answer 1

Hope this helps.......

Answer 2

Given,

(m+2n)²x²-22x(m+2n)+72

To find,

The factors of the given expression.

Solution,

The factors of (m+2n)²x²-22x(m+2n)+72 will be [(m+2n)x - 18] [ (m+2n)x - 4].

We can easily solve this problem by following the given steps.

According to the question,

(m+2n)²x²-22x(m+2n)+72

Now, we can factorize this expression by taking (m+2n) to be a and then by splitting the middle term such that their multiplication will give 72 × (m+2n)²x² and their addition will give -22x(m+2n).

So, these two terms will be -18x(m+2n) and -4x(m+2n).

(m+2n)²x²-22x(m+2n)+72

(m+2n)²x²-18x(m+2n)-4x(m+2n)+72

Now, putting a in place of (m+2n),

a²x²-18ax-4ax+72

Taking ax common from the first two terms and -4 common from the last two terms,

ax(ax-18) -4(ax-18)

Taking (ax-18) common,

(ax-18) (ax-4)

Now, replacing a by (m+2n),

[(m+2n)x - 18] [ (m+2n)x - 4]

Hence, the factors of (m+2n)²x²-22x(m+2n)+72 are [(m+2n)x - 18] [ (m+2n)x - 4].