How do you factor $16 + 40 x^{2} - 25 x^{4}$ $16+ 40x ^ { 2} - 25x ^ { 4}$ ?

Question

How do you factor $16 + 40 x^{2} - 25 x^{4}$ $16+ 40x ^ { 2} - 25x ^ { 4}$ ?

1 Answer

Impact of this question

1674 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-19T12:56:38

See the explanation below...

Explanation:

These type of polynomials can be factored by substitution.

Let's subtitute $u = x^{2}$ $u=x^2$ in the above polynomial, so that we get:

$= 25 u^{2} + 40 u + 16$ $=25u^2+40u+16$

We have to break the $40 u$ $40u$ into two terms, let's say $u$ $u$ and $v$ $v$ such that their sum must be equal to $40 u$ $40u$ and their product must be equal to the product of $25 u$ $25u$ and $16$ $16$ .

Since, $20 u + 20 u = 40 u$ $20u+20u=40u$ and $20 u \cdot 20 u = 400 u^{2}$ $20u\cdot 20u = 400u^2$ ,

we can write:

$= (25 u^{2} + 20 u) + (20 u + 16)$ $=(25u^2+20u)+(20u+16)$

Factor out $5 u$ $5u$ from left side terms and $4$ $4$ from right side terms, so that we get:

$= 5 u (5 u + 4) + 4 (5 u + 4)$ $=5u(5u+4)+4(5u+4)$

Factor out common term $(5 u + 4)$ $(5u+4)$ , so that we have left with:

$= (5 u + 4) (5 u + 4)$ $=(5u+4)(5u+4)$

Substitute back $u = x^{2}$ $u=x^2$ , and write as a square:

$= {(5 x^{2} + 4)}^{2}$ $=(5x^2+4)^2$

Which is our required factored form.

Science

Math

Humanities

... and beyond

How do you factor $16 + 40 x^{2} - 25 x^{4}$ $16+ 40x ^ { 2} - 25x ^ { 4}$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you factor 16+40x2−25x416+ 40x ^ { 2} - 25x ^ { 4}?

1 Answer

Explanation:

Related questions

Impact of this question

How do you factor $16 + 40 x^{2} - 25 x^{4}$ $16+ 40x ^ { 2} - 25x ^ { 4}$ ?