Nathan Maynard-Ellis, 30, and David Leesley, 25, tried cover their tracks after killing and dismembering Julia Rawson, 42, last year, Coventry Crown Court was told.
They hid her remains in overgrowth, changed carpets and underlay at their flat on Mission Drive, Tipton, and burnt their clothes, prosecutors allege.
Ms Rawson's remains were discovered at two sites in Tipton where efforts were made to hide the body parts, said Mr Karim Khalil QC, prosecuting. There was also evidence of some burning.
One site was in a woodland located at the rear of playing fields belonging to Sacred Heart Primary School, on Sedgley Road East, while the other was on wasteland off Coneygree Road.
Four bags were discovered across the two sites containing her body parts which included her head, torso, legs, hands and arms.
An examination of her skull revealed a fracture to her nasal bone while she also sustained a fracture to her neck region, said Mr Khalil. It was unclear whether these fractures came before her death.
Both defendants have admitted concealment of a corpse and perverting the course of justice by replacing bloodstained carpet and underlay at their flat.
Mr Khalil told the jury that both men visited Carpetright, in Oldbury, a day after Ms Rawson's murder on May 12, and told staff they wanted carpet "fitting urgently" at their flat.
One staff member described the pair as "an usual looking couple" and added the "transaction was unusual" as they went straight to the carpet they wanted.
Prosecutors allege both defendants acted together by burning clothing in the wake of the alleged killing. A neighbour reported "smelling burning" and saw both men in their garden, the court heard.
The couple also disposed of a blood-stained sofa where Ms Rawson lay either bleeding or was dismembered on, said Mr Khalil. It was said the dismemberment took place in the bathroom as well.
Following the killing, they carried on living their lives as normal, the court heard.
Mr Khalil said: "They went about their daily lives thereafter, we say, as if nothing untoward had happened - going to the pub, meeting family, going to work."