Question

Factorise: (z²+z+1/4)​

Answer 1

Answer:

Factor z^2+z+1/4

z2+z+14z2+z+14

Factor using the perfect square rule.

Tap for fewer steps...

Rewrite 11 as 1212.

z2+z+124z2+z+124

Rewrite 44 as 2222.

z2+z+1222z2+z+1222

Rewrite.

z2+z+(12)2z2+z+(12)2

Check the middle term by multiplying 2ab2ab and compare this result with the middle term in the original expression.

2ab=2⋅z⋅122ab=2⋅z⋅12

Simplify.

2ab=z2ab=z

Factor using the perfect squaretrinomial rule a2+2ab+b2=(a+b)2/2a2+2ab+b2=(a+b)2, where a=za=z and b=12b=1/2.

(z+1/2)2

Step-by-step explanation:

Answer 2

Answer:

$(z+\frac{1}{2})(z+\frac{1}{2})$

Step-by-step explanation:

Do you remember $(a+b)^2=a^2+2ab+b^2$?

If you look at the expression it is $z^2+z+\frac{1}{4}$

so $a^2=z^2$ and $2ab=z$ and $b^2=(\frac{1}{2})^2$

now you can write $(z+\frac{1}{2})^2$ , this means:

$(z+\frac{1}{2})(z+\frac{1}{2})$